## Big Ideas Math Book 3rd Grade Answer Key Chapter 15 Find Perimeter and Area

Big Ideas Math Book 3rd Grade Answer Key Chapter 15 Find Perimeter and Area answer key are attainable in this chapter. This answer key is useful for students who are preparing for their examinations and can download this pdf for free of cost. Here, each and every question was explained in detail which helps students to understand easily. Big Ideas Math Book 3rd Grade Answer Key Chapter 15 explains different types of questions on perimeter and area.

## Big Ideas Math Book 3rd Grade Answer Key Chapter 15 Find Perimeter and Area

This chapter contains different topics like finding the perimeter of the polygons, finding unknown side lengths and the same perimeter with different areas, etc. Those topics were being set up by the numerical specialists as indicated by the most recent release. Look down this page to get the answers for all the inquiries. Tap the connection to look at the subjects shrouded in this chapter Find Perimeter and Area.

**Lesson 1 Understand Perimeter**

**Lesson 2 Find Perimeters of Polygons**

**Lesson 3 Find Unknown Side Lengths
**

**Lesson 4 Same Perimeter, Different Areas**

- Lesson 15.4 Same Perimeter, Different Areas
- Same Perimeter, Different Areas Homework & Practice 15.4

**Lesson 5 Same Area, Different Perimeters**

- Lesson 15.5 Same Area, Different Perimeters
- Same Area, Different Perimeters Homework & Practice 15.5

**Performance Task
**

- Find Perimeter and Area Performance Task
- Find Perimeter and Area Activity
- Find Perimeter and Area Chapter Practice
- Find Perimeter and Area Cumulative practice 1 – 15
- Find Perimeter and Area Cumulative Steam Performance Task 1 – 15

### Lesson 15.1 Understand Perimeter

**Explore and Grow**

Question 1.

Model a rectangle on your geoboard. Draw the rectangle and label its side lengths. What is the distance around the rectangle?

Answer:

The units around the rectangle are 15 units.

Explanation:

In the above figure, the length of the rectangle is 4 units, and

the breadth of the rectangle is 3 units.

The units around the rectangle are 15 units.

**Structure**

Change the side lengths of the rectangle on your geoboard. What do you notice about the distance around your rectangle compared to the distance around the rectangle above? Explain

Answer:

The distance around the rectangle is 15 units

Explanation:

In the above figure, we can see the length of the rectangle is 3 units, and

the breadth of the rectangle is 4 units.

There is no change in the distance around the rectangle which is 15 units.

**Think and Grow: Understand Perimeter**

Perimeter is the distance around a ﬁgure. You can measure perimeter using standard units, such as inches, feet, centimeters, and meters.

**Example**

Find the perimeter of the rectangle.

Choose a unit to begin counting. Count each unit around the rectangle.

Answer:

The perimeter of the rectangle is 20 in.

Explanation:

To find the perimeter of the triangle, we need to know the length and the breadth of the rectangle.

Here, the length of the rectangle is 7 in,

and the breadth is 3 in,

So the perimeter of the rectangle is 2(Length + Breadth)

= 2(7+3)

= 2(10)

= 20 in.

**Show and Grow**

Question 1.

Find the perimeter of the figure.

There are ___ units around the figure.

Answer:

There are 22 units around the figure.

Explanation:

To find the perimeter of the rectangle, we need to know the length and the breadth of the rectangle.

Here, the length of the rectangle is 6 m,

and the breadth is 5 m,

So the perimeter of the rectangle is 2(Length + Breadth)

= 2(6+5)

= 2(11)

= 22 m.

Question 2.

There are ___ units around the figure.

So, the perimeter is ____ feet.

Answer:

The perimeter of the figure is 24 ft.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure

So the sides of the figure are 5,3,2,4,3,7.

and the perimeter of the figure is 5+3+2+4+3+7

= 24 ft.

Question 3.

Draw the figure that has a perimeter of 16 centimeters.

Answer:

The sides of the figure are 4 cm.

Explanation:

As the perimeter of the figure is 16 cm,

So let the sides of the figure be 4 cm,

by that, we can get the perimeter as 16 cm, i.e

4+4+4+4= 16 cm.

**Apply and Grow: Practice**

Question 4.

Find the perimeter of the ﬁgure.

There are ___ units around the figure.

So, the perimeter is ___

Answer:

There are 20 units around the figure.

So, the perimeter is 20 cm.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure

So the sides of the figure are 3,3,2,2,5,5.

and the perimeter of the figure is 3+3+2+2+5+5

= 20 units,

So the perimeter is 20 cm.

Question 5.

There are ___ units around the figure.

So, the perimeter is ___

Answer:

There are 26 units around the figure.

So, the perimeter is 26 ft.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure

So the sides of the figure is 5,5,2,3,1,3,2,5

and the perimeter of the figure is 5+5+2+3+1+3+2+5

= 26 units,

So the perimeter is 26 ft.

Question 6.

Perimeter = ___

Answer:

The perimeter of the figure is 22 in.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure

So the sides of the figure is 4,3,2,3,3,3,1,3

and the perimeter of the figure is 4+3+2+3+3+3+1+3

= 22 units,

So the perimeter is 22 in.

Question 7.

Perimeter = ___

Answer:

The perimeter is 24 m.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure

So the sides of the figure is 5,7,2,2,1,2,1,1,1,2

and the perimeter of the figure is 5+7+2+2+1+2+1+1+1+2

= 24 units,

So the perimeter is 24 m.

Question 8.

Draw a ﬁgure that has a perimeter likely measurement for the of 14 centimeters.

Answer:

The length of the rectangle is 2 cm, and

the breadth is 5 cm.

Explanation:

In the above figure, we can see the length of the rectangle is 2 cm

and the breadth of the rectangle is 5 cm

perimeter = 2(length + breadth)

= 2(5+2)

= 2(7)

= 14 cm.

so the perimeter of the rectangle is 14 cm.

Question 9.

**Precision** Which is the most likely measurement for the perimeter of a photo?

20 inches

100 meters

5 centimeters

2 inches

Answer:

2 inches.

Explanation:

The most likely measurement for the perimeter of a photo is 2 inches.

Question 10.

**You be the teacher** Your friend counts the units around the figure and says the perimeter is 12 units. Is your friend correct? Explain.

Answer:

No, he is not correct.

Explanation:

No, he is not correct. As there are 2+2+1+1+4+1+1+2= 14 units, but not 12 units. So he is not correct.

**Think and Grow: Modeling Real Life**

Use a centimeter ruler to ﬁnd the perimeter of the bookmark.

The perimeter is ___

Answer:

The perimeter of the bookmark is 26 cm.

Explanation:

On measuring, the length of the sides of the bookmark are 4 cm, 9 cm, 2 cm, 2 cm, 9 cm

to find the perimeter of the bookmark, we will add all the length of the sides

so the perimeter of the bookmark is

p = 4 cm+ 9 cm+ 2 cm+ 2 cm+ 9 cm

= 26 cm.

The perimeter of the bookmark is 26 cm.

**Show and Grow**

Question 11.

Use an inch ruler to find the perimeter of the decal.

Answer:

The perimeter of the decal is 17 in.

Explanation:

On measuring, the length of the sides of the decal is 5in, 2in, 5in, 5in

to find the perimeter of the decal, we will add all the length of the sides

so the perimeter of the decal is

p= 5in+2in+5in+5in

= 17 in

The perimeter of the decal is 17 in.

Question 12.

How much greater is the perimeter of your friend’s desk than the perimeter of your desk?

Answer:

Friend’s perimeter is 22-16= 6 times greater.

Explanation:

As we can see figure 1 is a square and the sides of the square are 4 ft.

So the perimeter of the square is a+a+a+a,

= 4+4+4+4

= 16 ft.

And now let’s find the perimeter of the friend’s figure,

So the sides of the figure is 2,6,5,2,3,4

and the perimeter is 2+6+5+2+3+4= 22 ft.

By this, we can see that the friend’s figure has a greater perimeter,

and friend’s perimeter is 22-16= 6 times greater.

Question 13.

**DIG DEEPER!**

Explain how you might use a centimeter ruler and string to estimate the perimeter of the photo of the window.

Answer:

Here, we will use the ruler to find the length of the bottom part of the window and the sides which are straight we can find the length using the ruler. And the curve sides we will measure using the string.

### Understand Perimeter Homework & Practice 15.1

Question 1.

There are ___ units around the figure.

So, the perimeter is ___ inches.

Answer:

There are 20 units around the figure,

So the perimeter is 20 in.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure,

As we can see the above image is a square,

and the perimeter of the square is s+s+s+s

= 5+5+5+5

= 20 in.

As there are 20 units around the figure,

So the perimeter is 20 in.

Question 2.

There are ___ units around the figure.

So, the perimeter is ___ feet.

Answer:

There are 32 units around the figure,

So the perimeter is 32 ft.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure,

The sides of the above figure is 2,3,4,3,2,5,8,5

and the perimeter of the figure is 2+3+4+3+2+5+8+5

= 32 units.

As there are 32 units around the figure,

So the perimeter is 32 ft.

Question 3.

Perimeter = ___

Answer:

There are 26 units around the figure,

So the perimeter is 26 cm.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure,

The sides of the above figure is 2,2,2,3,1,3,5,8

and the perimeter of the figure is 2+2+2+3+1+3+5+8

= 26 units.

As there are 26 units around the figure,

So the perimeter is 26 cm.

Question 4.

Perimeter = ___

Answer:

There are 38 units around the figure,

So the perimeter is 38 m.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure,

The sides of the above figure is 2,8,2,3,1,3,2,8,2,3,1,3

and the perimeter of the figure is 2+8+2+3+1+3+2+8+2+3+1+3

= 38 units.

As there are 38 units around the figure,

So the perimeter is 38 m.

Question 5.

Draw a figure that has a perimeter of 18 inches.

Answer:

The length of the rectangle is 5 in

and the breadth of the rectangle is 4 in.

Explanation:

Let the length of the rectangle be 5 in

and the breadth of the rectangle be 4 in

so the perimeter of the rectangle is

p = 2(length+breadth)

= 2(5+4)

= 2(9)

= 18 in.

Question 6.

**Reasoning**

Which color represents the perimeter of the rectangle? What does the other color represent?

Answer:

Blue color represents the perimeter of the rectangle and

the other color yellow represents the area of the figure.

Explanation:

In the above figure, the blue color represents the perimeter of the rectangle.

Because the perimeter represents the distance around the edge of the shape.

And the other color yellow represents the area of the figure,

as area represents the amount of space inside a shape.

Question 7.

Modeling Real Life

Use a centimeter ruler toﬁnd the perimeter of the library card.

Answer:

The perimeter of the library card is 24 cm.

Explanation:

On measuring, the length of the sides of the library card is 5cm, 7cm, 5cm, 7cm

to find the perimeter of the library card, we will add all the length of the sides

so the perimeter of the library card is

p= 5cm+7cm+5cm+7cm

= 24 cm

The perimeter of the library card is 24 cm.

Question 8.

Modeling Real Life

How much greater is the perimeter of your piece of fabric than the perimeter of your friend’ spiece of fabric?

Answer:

My fabric is 4 inches greater than my friend’s fabric.

Explanation:

To find the perimeter of the figure 1, we will add all the sides of the figure,

The sides of the above figure is 2,1,1,2,2,2,8,2,2,2,1,1

and the perimeter of the figure is 2+1+1+2+2+2+8+2+2+2+1+1

= 26 in.

So the perimeter of the figure is 26 in.

And now let’s find the perimeter of the friend’s figure,

So the sides of the figure is 1,2,2,4,1,5,4,3

and the perimeter is 1+2+2+4+1+5+4+3

= 22 in.

By this, we can see that my fabric has the highest perimeter than the friend’s fabric

which is 26-22= 4 in greater.

**Review & Refresh**

Write two equivalent fractions for the whole number.

Question 9.

Answer:

1= 4/4 = 6/6

Explanation:

Here, the equivalent fraction for the whole number means if the numerator was divided by the denominator without any reminder then the fraction is equivalent to a whole number. So 1= 4/4 = 6/6.

Question 10.

Answer:

4= 4/1 = 8/2.

Explanation:

Here, the equivalent fraction for the whole number means if the numerator was divided by the denominator without any reminder then the fraction is equivalent to a whole number. So 4= 4/1 = 8/2.

Question 11.

Answer:

6= 24/4 = 36/6.

Explanation:

Here, the equivalent fraction for the whole number means if the numerator was divided by the denominator without any reminder then the fraction is equivalent to a whole number. So 6= 24/4 = 36/6.

### Find Perimeters of Polygons 15.2

**Explore and Grow**

Model a rectangle on your geoboard. Draw the rectangle and label its side lengths. Then ﬁnd the perimeter in more than one way.

Answer:

The perimeter of the rectangle is 14 units.

Explanation:

In the above figure, we can see the length of the rectangle is 4 units

and the breadth of the rectangle is 3 units,

so the perimeter of the rectangle is

p =2(length + breadth)

= 2(4+3)

= 2(7)

= 14 units.

The perimeter of the rectangle is 14 units.

**Critique the Reasoning of Others**

Compare your methods of ﬁnding the perimeter to your partner’s methods. Explain how they are alike or different.

Answer:

There are two methods to find the perimeter explained below.

Explanation:

There are two ways to find the perimeter.

The first method is

Perimeter = 2(length + breadth)

here, we will add length and breadth, and then we will multiply the result by 2.

and the second method is

Perimeter = a+b+c+d

here, we will add all the sides of the figure.

**Think and Grow: Find Perimeter**

Example

Find the perimeter of the trapezoid.

You can find the perimeter of a figure by adding all of the side lengths.

Write an equation. The letter P represents the unknown perimeter. Add the side lengths.

So, the perimeter is ___.

Answer:

So, the perimeter is 36 in.

Explanation:

To find the perimeter of the trapezoid, we will add all the sides of the trapezoid,

so the sides of the trapezoid is 6 in,12 in,8 in,10 in

The perimeter is 6+12+8+10

= 36 in.

Example

Find the perimeter of the rectangle

Because a rectangle has two pairs of equal sides, you can also use multiplication to solve.

One Way:

Another Way:

So, the perimeter is ___.

Answer:

Perimeter = 7+9+7+9

= 32 cm.

Perimeter= 2×9 + 2× 7

= 32 cm.

So, the perimeter is 32 cm.

Explanation:

To find the perimeter of a rectangle, we have two ways,

One way is to add all the sides of the rectangle, which is

7+9+7+9= 32 cm.

And the other way is, as the two sides of the rectangle are equal, we wil use formula

Perimeter = 2( Length + Breadth)

= 2× Length + 2 × Breadth

= 2×9 + 2× 7

= 18+ 14

= 32 cm.

**Show and Grow**

Find the perimeter of the polygon.

Answer:

Explanation:

To find the perimeter of the polygon, we will add the length of the all sides.

Question 1.

The perimeter is ___.

Answer:

The perimeter is 12 m.

Explanation:

To find the perimeter of the polygon, we will add the length of all sides of the polygon.

So the length of the sides is 5 m, 3 m, 3 m, 2 m

The perimeter is 5+3+3+2

= 12 m.

Question 2.

The perimeter is ___.

Answer:

The perimeter is 24 ft.

Explanation:

As we can see in the above figure which has all sides are equal,

so the perimeter of the square is 4s

= 4×6

= 24 ft.

**Apply and Grow: Practice**

Find the perimeter of the polygon.

Question 3.

Perimeter = ___

Answer:

The perimeter of the polygon is 28 m.

Explanation:

To find the perimeter of the polygon, we will add the length of the all sides of the polygon.

So the length of the sides is 4 m, 9 m, 10 m, 5 m

The perimeter is 4+9+10+5

= 28 m.

Question 4.

Perimeter = ___

Answer:

The perimeter of the figure is 40 in.

Explanation:

To find the perimeter of the figure, we will add the length of all sides of the figure.

So the length of the sides is 12 in, 4 in, 8 in, 7 in,9 in.

The perimeter is 12+4+8+7+9

= 40 in.

Question 5.

Rectangle

Perimeter = ___

Answer:

The perimeter of the rectangle is 36 cm.

Explanation:

To find the perimeter of the rectangle, we need to know the length and the breadth of the rectangle.

Here, the length of the rectangle is 9 cm,

and the breadth is 10 cm,

So the perimeter of the rectangle is 2(Length + Breadth)

= 2(10+9)

= 2(19)

= 38 cm.

Question 6.

Rhombus

Perimeter = ___

Answer:

The perimeter of the Rhombus is 4 in.

Explanation:

As all sides of the Rhombus are equal, so the formula of the Rhombus is 4a

and the side of the Rhombus is 1 in,

so the perimeter is 4a

= 4×1

= 4 in.

Question 7.

Parallelogram

Perimeter = ___

Answer:

The perimeter of the parallelogram is 22 cm.

Explanation:

As the opposite sides of the parallelogram are equal,

so the perimeter of the parallelogram is 2(a+b)

the length of the parallelogram is 3 cm,

and the breadth of the parallelogram is 8 cm

So the perimeter of the parallelogram is

= 2(3+8)

= 2(11)

= 22 cm.

Question 8.

Square

Perimeter = ___

Answer:

The perimeter of the square is 16 ft.

Explanation:

As we can see in the above figure which has all sides are equal,

so the perimeter of the square is 4s

= 4×4

= 16 ft.

Question 9.

You build a pentagon out of wire for a social studies project. Each side is 8 centimeters long. What is the perimeter of the pentagon?

Answer:

The perimeter of the pentagon is 40 cm.

Explanation:

The length of the pentagon is 8 cm,

so the perimeter of the pentagon is 5a,

which is 5×8

= 40 cm

Question 10.

**Number Sense**

The top length of the trapezoid is 4 feet. The bottom length is double the top. The left and right lengths are each 2 feet less than the bottom. Label the side lengths and ﬁnd the perimeter of the trapezoid.

Answer:

The sides of the trapezoid are 4ft, 6ft, 8ft, 6ft, and the perimeter is 24 ft.

Explanation:

As the top length of the trapezoid is 4 feet and the bottom length is double the top,

which is 4×2= 8 feet. And the left and right lengths are each 2 feet less than the bottom,

which means 8 – 2 = 6 ft each.

So to find the perimeter of the trapezoid is we will add the length of all sides.

The perimeter of the trapezoid is 4+6+8+6= 24 ft.

Question 11.

**Writing**

Explain how finding the perimeter of a rectangle is different from finding its area.

Answer:

Perimeter= 2(length + breadth)

Area = length × breadth.

Explanation:

To find the perimeter of the rectangle,

we will add the length and breadth and will multiply the result with 2

Perimeter= 2(length + breadth)

and to find the area of the rectangle,

we will multiply the length and breadth of the rectangle.

Area = length × breadth.

Question 12.

**Dig Deeper!**

A rectangle has a perimeter of 12 feet. What could its side lengths be ?

Answer:

The length of the rectangle is 4 feet

and the breadth of the rectangle is 2 feet

Explanation:

Given the perimeter is 12 feet,

so the let the length be 4 feet

and the breadth be 2 feet

Let’s check on the length and breadth is correct are not

perimeter = 2( length + breadth)

= 2( 4+2)

= 2(6)

= 12 feet.

**Think and Grow: Modeling Real Life**

The rectangular sign is 34 feet longer than it is wide. What is the perimeter of the sign?

Understand the problem:

Make a plan:

Solve:

The perimeter is ___.

Answer:

The perimeter of the rectangular sign is 124 ft.

Explanation:

Given the rectangular sign is 34 feet longer than it’s wide

and the wide is 14 ft,

so the length is 34ft + 14ft= 48 ft.

the perimeter of the rectangular sign is

P= 2(48ft + 14ft)

= 2(62ft)

= 124 ft.

The perimeter of the rectangular sign is 124 ft.

**Show and Grow**

Question 13.

A city has a rectangular sidewalk in a park. The sidewalk is 4 feet wide and is 96 feet longer than it is wide. What is the perimeter of the sidewalk?

Answer:

The perimeter of the sidewalk is 208 feet.

Explanation:

As given the rectangular sidewalk’s wide is 4 feet and the length is 96 feet longer than it’s wide,

which means 96+4= 100 feet is the length of the rectangular sidewalk,

so the perimeter of the rectangular sidewalk is 2( length + breadth)

= 2( 4+100)

= 2(104)

= 208 feet.

Question 14.

A team jogs around a rectangular field three times. The field is 80 yards long and 60 yards wide. How many yards does the team jog?

Answer:

The number of yards does the team jog is 3×280= 840 yards.

Explanation:

The length of the rectangular field is 80 yards,

The breadth of the rectangular field is 60 yards,

So, the perimeter of the rectangular field is 2(length + breadth)

= 2(80+60)

= 2(140)

= 280 yards.

As the team jogs around a rectangular field three times,

so the number of yards does the team jog is 3×280= 840 yards.

Question 15.

Each side of the tiles is 8 centimeters long. What is the sum of the perimeters?

You put the tiles together as shown. Is the perimeter of this new shape the same as the sum of the perimeters above? Explain.

Answer:

The sum of the perimeters is 96 cm.

Yes, there will be a change in the perimeter of the new figure. The perimeter is 80 cm.

Explanation:

In the above figure, we can see a hexagon that has six sides.

So the formula for the perimeter of a hexagon is 6a,

the perimeter of the tiles is 6×8

= 48 cm.

So the sum of the tiles 48+48= 96 cm.

Yes, there will be a change in the perimeter of the new figure. As there are ten sides in the new figure, so the perimeter of the new figure is 10×8= 80 cm.

### Find Perimeters of Polygons Homework & Practice 15.2

Find the perimeter of the polygon

Question 1.

Perimeter = ___

Answer:

The perimeter of the polygon is 29 in.

Explanation:

The perimeter of the polygon is the sum of the length of its sides,

So the sides of the polygon are 9 in, 4 in, 6 in, 10 in,

and the perimeter of the polygon is 9+4+6+10= 29 in.

Question 2.

Perimeter = ___

Answer:

The perimeter of the figure is 38 cm.

Explanation:

The perimeter of the figure is the sum of the length of its sides,

So the sides of the figure are 6 cm, 5 cm, 7 cm, 8 cm, 7 cm, 5 cm,

and the perimeter of the figure is 6+5+7+8+7+5= 38 cm.

Question 3.

Square

Perimeter = ___

Answer:

The perimeter of the square is 8 ft.

Explanation:

The length of the square is 2 ft,

and the perimeter of the square is 4a

= 4×2

= 8 ft.

so the perimeter of the square is 8 ft.

Question 4.

Parallelogram

Perimeter = ___

Answer:

The perimeter of the parallelogram is 8m.

Explanation:

The length of the parallelogram is 1 m,

and the breadth of the parallelogram is 3 m,

so the perimeter of the parallelogram is 2(length + breadth)

= 2(1+3)

= 2(4)

= 8 m.

Question 5.

Rhombus

Perimeter = ___

Answer:

The perimeter of the rhombus is 40 ft.

Explanation:

The length of the side of the rhombus is 10 ft,

and the perimeter of the rhombus is 4a

= 4×10

= 40 ft.

Question 6.

Perimeter = ___

Answer:

The perimeter of the rectangle is 22 in.

Explanation:

To find the perimeter of the rectangle, we need to know the length and the breadth of the rectangle.

Here, the length of the rectangle is 7 in,

and the breadth is 4 in,

So the perimeter of the rectangle is 2(Length + Breadth)

= 2(7+4)

= 2(11)

= 22 in.

Question 7.

Each side of a triangle is 5 centimeters long. What is the perimeter of the triangle?

Answer:

The perimeter of the triangle is 15 cm.

Explanation:

Given the length of the side of the triangle is 5 cm,

and the perimeter of the triangle is 3a

= 3×5

= 15 cm.

Question 8.

**You Be The Teacher**

Descartes says that a square will always have a greater perimeter than a triangle because it has more sides. Is he correct? Explain.

Answer:

Yes, Descartes is correct.

Explanation:

Yes, Descartes is correct. As the square has four sides and the perimeter of the square is 4a.

Whereas the triangle has 3 sides and the perimeter of the triangle is 3a.

So the square will always have a greater perimeter than a triangle.

Question 9.

**Structure**

Draw a pentagon and label its sides so that it has the same perimeter as the rectangle.

Answer:

The length of the side of the pentagon is 4m.

Explanation:

Given the length of the rectangle is 7 m,

and the breadth of the rectangle is 3 m,

So the perimeter of the rectangle is 2( length + breadth)

= 2(7+3)

= 2(10)

= 20 m.

Here we have the perimeter of the pentagon which is 20 m,

so we should find the sides of the pentagon,

As we know the perimeter of the pentagon is 5a

5a= 20

a= 20/5

= 4 m.

So the length of the side of the pentagon is 4m.

Question 10.

**Modeling Real Life**

An Olympic swimming pool is 82 feet longer than it is wide. What is the perimeter of the swimming pool?

Answer:

The perimeter of the swimming pool is 492 ft.

Explanation:

Given the Olympic swimming pool is 82 feet longer than it’s wide

and the wide is 82 ft,

so the length of the swimming pool is 82+82= 164 ft

the perimeter of the swimming pool is

p= 2(length+breadth)

= 2(164+82)

= 2(246)

= 492 ft.

The perimeter of the swimming pool is 492 ft.

Question 11.

Modeling Real Life

You put painter’s tape around two rectangular windows. The windows are each 52 inches long and 28 inches wide. How much painter’s tape do you need?

Answer:

The painter’s tape 160 inches.

Explanation:

Given the length of the window is 52 inches

and the width of the window is 28 inches

so the perimeter of the window is

p= 2(length + breadth)

= 2(52+28)

= 2(80)

= 160 inches.

So the painter’s tape 160 inches.

**Review & Refresh**

Question 12.

Answer:

737.

Explanation:

On adding 590+147 we will get 737.

Question 13.

Answer:

894.

Explanation:

On adding 636+258 we will get 894

Question 14.

Answer:

805.

Explanation:

On adding 476+329 we will get 805

### Lesson 15.3 Find Unknown Side Lengths

**Explore and Grow**

You have a map with the three side lengths shown. The perimeter of the map is 20 feet. Describe how you can ﬁnd the fourth side length of your map without measuring.

Answer:

The fourth side of the map is 4ft.

Explanation:

We can find the value of the fourth side in two methods

First method:

Given the perimeter of the map is 20 feet,

and the sides of the map is 6 ft, 4 ft, 6ft, X ft.

As we know the perimeter of the rectangle is

6+4+6+X= 20 feet

16+X= 20

X= 20- 16

= 4 ft.

Second method:

As we know that the opposite sides of the rectangle are equal, as we know that the length of the side is 4 ft so the other side will also be 4 ft.

**Repeated Reasoning**

How is finding the unknown side length of a square different from finding the unknown side length of a rectangle?

Answer:

Refer below for a detailed explanation.

Explanation:

To find the unknown side length of the square

if we know the perimeter of the square then

the perimeter of the square is

p= 4a

we will substitute the value of p, on solving we will get the length of the square.

and to find the unknown side length of the rectangle,

we need to know the area or perimeter of the rectangle

and the other side of the rectangle.

so the formula of the perimeter of the rectangle is

p = 2(length + breadth)

we will substitute the perimeter value and the other side value

then we can find the length of the rectangle.

**Think and Grow: Find Unknown Side Lengths**

**Example**

The perimeter of the trapezoid is 26 feet. Find the unknown side length.

Write an equation for the perimeter.

Add the known side lengths.

What number plus 16 equals 26?

The unknown side length is ___.

Answer:

K= 10,

The number 16+10 equals 26.

The unknown side length is 10.

Explanation:

Given the perimeter of the trapezoid is 26 ft,

So the perimeter of the trapezoid is

K+5+6+5= 26

K+16= 26

K= 10.

The number 16+10 equals 26.

The unknown side length is 10.

Example

The perimeter of the square is 32 centimeters. Find the length of each side of the square.

Write an equation for the perimeter 4 times what number equals 32?

So, the length of each side is ___.

Answer:

n= 8.

The length of each side is 8 cm.

Explanation:

The perimeter of the square is 32 cm

So to find the sides of the square

4a= 32

a= 32/4

= 8 cm.

So, the length of each side is 8 cm.

**Show and Grow**

Find the unknown side length.

Question 1.

Perimeter = 34 inches

y = ___

Answer:

y = 13 in.

Explanation:

Given the perimeter is 34 inches,

and the sides of the figure are 10 in, 7 in, 4 in, y in.

so the perimeter of the figure is

34 in = 10+7+4+y

34 = 21+ y

y = 34 – 21

y = 13.

Question 2.

Perimeter = 20 meters

j = ___

Answer:

The length of the sides of the square is 5 m.

Explanation:

As we can see the above figure is a square and the perimeter of the square 20 meters,

so the sides of the square are

perimeter = 4a

20 = 4 j

j= 5 m.

**Apply and Grow: Practice**

Find the unknown side length.

Question 3.

Perimeter = 19 feet

y = ___

Answer:

The perimeter of the figure is 8 ft.

Explanation:

The perimeter of the figure is 19 feet,

and the length of the sides of the figure is 8 ft, 3 ft, y ft.

so perimeter = 8 ft + 3 ft + y ft

19= 11 ft + y ft

y= 19 ft – 11 ft

= 8 ft.

Question 4.

Perimeter = 26 centimeters

d = ___

Answer:

d= 4 cm.

Explanation:

The perimeter of the figure is 26 cm,

and the length of the sides of the figure is 10 cm, 5 cm, 7 cm, d cm.

so the perimeter of the figure is

p = 10+5+7+d

26 = 22 + d

d= 26-22

= 4

Question 5.

Perimeter = 30 feet

k = ___

Answer:

k = 11 ft.

Explanation:

Given the perimeter of the figure is 30 feet,

and the length of the sides is 5ft, 12 ft, 2 ft, k ft

So the perimeter of the figure is

p = 5 + 12 + 2 + k

30 ft = 19 ft + k

k = 11 ft.

Question 6.

Perimeter = 32 inches

k = ___

Answer:

k= 4 in.

Explanation:

Given the perimeter of the figure is 32 inches,

and the lengths of all sides is 10 in, 4 in, 5 in, 4 in, 5 in, k in.

So the perimeter of the figure is

p= 10+4+5+4+5+k

32 in = 28 in + k

k= 4 in.

Question 7.

Perimeter = 8 meters

y = ___

Answer:

y = 2 m.

Explanation:

Given the perimeter of the rhombus is 8 feet,

and the length of the side is y m,

So the perimeter of the rhombus is

p = 4a

8 m = 4×y

y = 2 m.

Question 8.

Perimeter = 48 inches

d = ___

Answer:

d = 8 in.

Explanation:

Given the perimeter of the Hexagon is 48 inches,

and the length of the sides is d in

So the perimeter of the hexagon is

p = 6 a

48 in = 6 × d in

d= 8 in.

Question 9.

**Number Sense**

A rectangle has a perimeter of 30 centimeters. The left side is 7 centimeters long. What is the length of the top side?

Answer:

The length of the top side is 8 cm.

Explanation:

Given the perimeter of the rectangle is 30 cm,

and the length of the left side of the rectangle is 7 cm,

So let the length of the top side be X,

Perimeter of the rectangle is

P = 2 (Length + breadth)

30 = 2 ( 7 cm + X cm)

30 / 2 = 7 cm + X cm

15 = 7 cm + X cm

X = 15 cm – 7 cm

X = 8 cm.

so, the length of the top side is 8 cm.

Question 10.

**Writing**

A triangle has three equal sides and a perimeter of 21 meters. Explain how to use division to ﬁnd the side lengths.

Answer:

The length of the side is 7 m.

Explanation:

Given the perimeter of the triangle is 21 m,

and we need to find the side of the lengths,

so the perimeter of the triangle is

p = 3a

21 m = 3×a

a = 21/3

= 7 m

So the length of the side is 7 m.

Question 11.

**DIG DEEPER!**

Newton draws and labels the square and rectangle below. The perimeter of the combined shape is 36 feet. Find the unknown side length.

Answer:

The unknown side of the length is 14 ft.

Explanation:

As the perimeter of the combined shape is 36 feet,

and the length of the side of the rectangle is 4 ft, and the other side be X ft

and the perimeter of the rectangle is 36 ft,

so perimeter = 2 (length + breadth)

36 ft = 2( 4 ft + X ft)

36/2 = 4 ft + X ft

18 = 4 ft + X ft

X= 14 ft.

The unknown side of the length is 14 ft.

**Think and Grow: Modeling Real Life**

The perimeter of the rectangular vegetable garden is 30 meters. What are the lengths of the other three sides?

Understand the problem:

Make a plan:

Solve:

The lengths of the other three sides are ___, ___, and ___.

Answer:

The lengths of other three sides is 6 m, 9 m, 9 m.

Explanation:

The perimeter of the rectangular vegetable garden is 30 m

as it is in a rectangular shape, so the opposite sides are equal,

and the length of the side of the rectangular vegetable garden is 6m,

let the other side be X m

so the perimeter is

p = 2( length + breadth)

30 m = 2( 6 m+ X m)

30/2 = 6 + X

15 = 6 + X

X= 15 – 6

= 9 m.

So the lengths of other three sides is 6 m, 9 m, 9 m.

**Show and Grow**

Question 12.

The perimeter of the rectangular zoo enclosure is 34 meters. What are the lengths of the other three sides?

Answer:

The lengths of the other three sides are 12 m, 11 m, 11 m.

Explanation:

The perimeter of the rectangular zoo is 34 m

as it is in rectangular shape, so the opposite sides are equal,

and the length of the side of the rectangular zoo is 12 m,

let the other side be X m

so the perimeter is

p = 2( length + breadth)

34 m = 2( 12 m+ X m)

34/2 = 12 + X

17 = 6 + X

X= 17 – 6

= 11 m.

So the lengths of the other three sides is 12 m, 11 m, 11 m.

Question 13.

The floor of an apartment is made of two rectangles. The Perimeter is 154 feet. What are the lengths of the other three sides?

Answer:

The other length of the side of the small rectangle is 7 ft.

The other length of the side of the big rectangle is 30 ft.

Explanation:

Given the perimeter of the apartment is 154 feet,

first, we will take the big rectangle,

as the opposite sides of the rectangle are equal and the length of the big rectangle is 30 ft

so the other length is also 30 ft.

as the perimeter of the small rectangle is 38 ft

and the length of the one side of the rectangle is 12 ft

so the other length of the small rectangle is

p = 2(length+breadth)

38 = 2(12 + breadth)

38/2 = 12+ breadth

19= 12 + breadth

breadth= 19 – 12

= 7 ft.

The other length of the side is 7 ft.

Question 14.

**DIG DEEPER!**

You want to make a flower bed in the shape of a pentagon. Two sides of the flower bed are each 7 inches long, and two sides are each 16 inches long. The perimeter is 57 inches. Sketch the flower bed and label all of the side lengths.

Answer:

The length of the other side is 11 ft.

Explanation:

Given the perimeter of the flower bed shaped pentagon is 57 inches

and the two sides of the flower bed each is 7 inches long

and the other two sides of the flower bed each is 16 inches long

the other side of the flower bed be X

the perimeter of the flower bed is

p = 7+7+16+16+X

57= 46+X

X= 11 in.

The length of the other side is 11 ft.

### Find Unknown Side Lengths Homework & Practice 15.3

Find the unknown side length.

Question 1.

Perimeter = 24 feet

d = ___

Answer:

The length of the unknown side is 8 ft.

Explanation:

The perimeter of the triangle is 24 ft,

and the lengths of the sides is 10 ft, 6 ft, d ft

so the perimeter of the triangle is

p = 10+6+d

24 = 10+6+d

24 = 16+d

d = 24 – 16

= 8 ft.

The length of the unknown side is 8 ft.

Question 2.

Perimeter = 46 inches

k = ___

Answer:

The length of the unknown side is 15 in.

Explanation:

The perimeter of the figure is 46 inches,

and the lengths of the sides is 13 in, 5 in, 13 in, k in

so the perimeter of the figure is

p = 13+5+13+k

46 = 31+k

46-31 = k

k = 15

= 15 in.

The length of the unknown side is 15 in.

Question 3.

Perimeter = 21 centimeters

y = ___

Answer:

The length of the unknown side is 7 cm.

Explanation:

The perimeter of the figure is 21 cm,

and the lengths of the sides is 4 cm, 1 cm, 9 cm, y cm

so the perimeter of the figure is

p = 4 cm+ 1 cm+ 9 cm+ y cm

21 = 14+ y

y = 21 – 14

y = 7

= 7 cm.

The length of the unknown side is 7 cm.

Question 4.

Perimeter = 41 meters

y = ___

Answer:

The length of the unknown side is 8 m.

Explanation:

The perimeter of the figure is 41 m,

and the lengths of the sides is 3 m, 12 m, 10 m, 8 m, y m

so the perimeter of the figure is

p = 3+12+10+8+y

41 = 33 + y

y = 41-33

y = 8

= 8 m.

The length of the unknown side is 8 m.

Question 5.

Perimeter = 12 feet

d = ___

Answer:

The length of the sides of the triangle is 4 ft.

Explanation:

The perimeter of the triangle is 12 feet,

and the length of the side of the triangle is d ft,

so the perimeter of the triangle is

p = 3 a

12 = 3 × d

d = 12/3

= 4 ft.

The length of the sides of the triangle is 4 ft.

Question 6.

Perimeter = 50 inches

k = ___

Answer:

The length of the sides of the Hexagon is 4 in.

Explanation:

The perimeter of the Hexagon is 50 inches,

and the length of the side of the Hexagon is k in,

so the perimeter of the hexagon is

p = 5 a

50 = 5 × k

k = 50/5

= 10 in.

The length of the sides of the triangle is 10 in.

Question 7.

**DIG DEEPER!**

Each polygon has equal side lengths that are whole numbers. Which polygon could have a perimeter of 16 centimeters? Explain.

Answer:

The length of the sides of the octagon is 2 cm.

Explanation:

In the above three polygons, the second figure is an octagon, which has eight sides.

and the perimeter of the octagon is

p = 8 a

16 cm = 8 a

a = 16 /8

= 2 cm.

Question 8.

**Number Sense**

The area of a square is 25 square inches. What is its perimeter?

Answer:

The perimeter of the square is 20 inches.

Explanation:

The area of the square is 25 square inches, so

area = s^2

25 = s^2

s= 5 inches

so the perimeter of the square is

p = 4s

= 4×5

= 20 inches.

Question 9.

**Modeling Real Life**

The perimeter of the rectangular side walk is 260 meters. What are the lengths of the other three sides?

Answer:

The length of the other three sides is 10 m,10m,120 m.

Explanation:

The perimeter of the rectangular side walk is 260 meters,

and the length of the one side of the side walk is 120 m,

so the perimeter of the rectangular side walk is

p = 2( length + breadth)

260 = 2 ( 120 + breadth)

260/2 = 120 + breadth

130 = 120 + breadth

breadth = 130 – 120

= 10 m.

The length of the other three sides is 10 m,10m,120 m.

Question 10

**Modeling Real Life**

Two rectangular tables are pushed together. The perimeter is 40 feet. What are the lengths of the other three sides?

Answer:

The other length of the side of the small rectangle is 3 ft.

The other length of the side of the big rectangle is 5 ft.

Explanation:

Given the perimeter of the apartment is 40 feet,

first, we will take the big rectangle,

as the opposite sides of the rectangle are equal

and the length of the big rectangle is 5 ft

so the other length is also 5 ft.

as the perimeter of the small rectangle is 10 ft

and the length of the one side of the rectangle is 2 ft

so the other length of the small rectangle is

p = 2(length+breadth)

10 = 2(2 + breadth)

10/2 = 2+ breadth

5= 2 + breadth

breadth= 5 – 2

= 3 ft.

The other length of the side is 3 ft.

**Review & Refresh**

Write the time. Write another way to say the time.

Question 11.

Answer:

06: 48

Explanation:

Another way to say time is 06: 48

Question 12.

Answer:

03: 24

Explanation:

Another way to say time is 03: 24

Question 13.

Answer:

Explanation:

Another way to say the time is 11: 48

### Lesson 15.4 Same Perimeter, Different Areas

Use color tiles to create two different rectangles that each have a perimeter of 16 units. Then draw your rectangles and label their dimensions. Do the rectangles have the same area? Explain how you know.

Answer:

No, the area of rectangle 1 and rectangle 2 is not the same.

Explanation:

Given the perimeter of the rectangle is 16 units

The length of rectangle 1 is 5 units

and the breadth of rectangle 1 is 3 units

so the area of rectangle 1 is

area = length × breadth

= 5×3

= 15 square units.

The length of rectangle 2 is 6 units

and the breadth of rectangle 2 is 2 units

so the area of rectangle 2 is

area = length × breadth

= 6×2

= 12 square units.

No, the area of rectangle 1 and rectangle 2 is not the same.

**Repeated Reasoning**

Draw another rectangle that has the same perimeter but different dimensions. Compare the area of the new rectangle to the rectangles above. What do you notice?

Answer:

No, the area of rectangle 1 and rectangle 2 is not the same.

Explanation:

The length of rectangle 1 is 4 units

and the breadth of rectangle 1 is 3 units

the perimeter of rectangle 1 is

p= 2(length+breadth)

= 2(4+3)

= 2(7)

= 14 units.

so the area of rectangle 1 is

area = length × breadth

= 4×3

= 12 square units.

The length of rectangle 2 is 5 units

and the breadth of rectangle 2 is 2 units

the perimeter of rectangle 1 is

p= 2(length+breadth)

= 2(5+2)

= 2(7)

= 14 units.

so the area of rectangle 2 is

area = length × breadth

= 5×2

= 10 square units.

No, the area of rectangle 1 and rectangle 2 is not the same.

**Think and Grow : Same Perimeter, Different Areas**

**Example :**

Find the perimeter and the area of Rectangle A. Draw a different rectangle that has the same perimeter. Which rectangle has the greater area?

Rectangle ___ has a greater area.

Answer:

The perimeter of the rectangle A is 20 m

and the area of the rectangle A is 24 m^{2}

The perimeter of rectangle B is 20 m

and the area of the rectangle B is 16 m^{2}

The rectangle A has a greater area.

Explanation:

Given the length of the rectangle is 6m

and the breadth of the rectangle is 4m,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(6 + 4)

= 2(10)

= 20 m.

And the area of the rectangle is

a = length × breadth

= 6 × 4

= 24 m^{2}

we can see in the above figure another rectangle with a length of 8m,

and the breadth is 2m,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(8 + 2)

= 2(10)

= 20 m.

And the area of the rectangle is

area = length × breadth

= 8×2

= 16 m^{2}

So the rectangle A has a greater area.

**Show and Grow**

Question 1.

Find the perimeter and area of Rectangle A. Draw a different rectangle that has the same perimeter. Which rectangle has the greater area?

Perimeter = ___

Area = ___

Perimeter = ___

Area = ___

Rectangle ___ has the greater area.

Answer:The perimeter of the rectangle A is 14 in

and the area of the rectangle A is 10 in^{2}

The perimeter of rectangle B is 14 in

and the area of the rectangle B is 12 in^{2}

The rectangle B has a greater area.

Explanation:

Given the length of the rectangle is 5 in

and the breadth of the rectangle is 2 in,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(5 + 2)

= 2(7)

= 14 in.

And the area of the rectangle is

a = length × breadth

= 5×2

= 10 in^{2}

we can see in the above figure another rectangle with a length of 4 in,

and the breadth is 3 in,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(4 + 3)

= 2(7)

= 14 in.

And the area of the rectangle is

area = length × breadth

= 4×3

= 12 in^{2}

So the rectangle B has a greater area.

**Apply and Grow: Practice**

Find the perimeter and area of Rectangle A. Draw a different rectangle that has the same perimeter. Which rectangle has the greater area?

Question 2.

Rectangle A

Perimeter = ___

Area = ___

Perimeter = ___

Area = ___

Rectangle ___ has the greater area.

Answer:

The perimeter of the rectangle A is 22 cm

and the area of the rectangle A is 11 cm^{2}

The perimeter of rectangle B is 22 cm

and the area of the rectangle B is 30 cm^{2}

The rectangle B has a greater area.

Explanation:

Given the length of the rectangle is 10 cm,

and the breadth of the rectangle is 1 cm,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(10 + 1)

= 2(11)

= 22 cm.

And the area of the rectangle is

a = length × breadth

= 11 × 1

= 11 cm^{2}

we can see in the above figure another rectangle with a length of 6 cm,

and the breadth is 5 cm,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(6 + 5)

= 2(11)

= 22 cm.

And the area of the rectangle is

area = length × breadth

= 6×5

= 30 cm^{2}

So the rectangle B has a greater area.

Question 3.

Rectangle A

Perimeter = ___

Area = ___

Rectangle B

Perimeter = ___

Area = ___

Rectangle ___ has the greater area

Answer:

The perimeter of the rectangle A is 20 m

and the area of the rectangle A is 21 m^{2}

The perimeter of rectangle B is 20 m

and the area of the rectangle B is 24 m^{2}

The rectangle B has a greater area.

Explanation:

Given the length of the rectangle is 7 m,

and the breadth of the rectangle is 3 m,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(7 + 3)

= 2(10)

= 20 m.

And the area of the rectangle is

a = length × breadth

= 7 × 3

= 21 m^{2}

we can see in the above figure another rectangle with a length of 6 m,

and the breadth is 4 m,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(6 + 4)

= 2(10)

= 20 m.

And the area of the rectangle is

area = length × breadth

= 6×4

= 24 m^{2}

So the rectangle B has a greater area.

Question 4.

MP Structure

Draw a rectangle that has the same perimeter as the one shown, but with a lesser area. What is the area ?

Answer:

The perimeter of the rectangle A is 26 ft

and the area of the rectangle A is 40 ft^{2}

The perimeter of rectangle B is 26 ft

and the area of the rectangle B is 30 ft^{2}

The rectangle B has a greater area.

Explanation:

Given the length of the rectangle is 5 ft,

and the breadth of the rectangle is 8 ft,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(5 + 8)

= 2(13)

= 26 ft.

And the area of the rectangle is

a = length × breadth

= 5 × 8

= 40 ft

we can see in the above figure another rectangle with a length of 10 ft,

and the breadth is 3 ft,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(10 + 3)

= 2(13)

= 26 ft.

And the area of the rectangle is

area = length × breadth

= 10×3

= 30 ft^{2}

So the rectangle A has a greater area.

**Think and Grow: Modeling Real Life**

A paleontologist has 12 meters of twine to rope off a rectangular section of the ground. How long and wide should she make the roped-off section so it has the greatest possible area?

Draw to show:

She should make the roped-off section ___ meters long and ___ meters wide.

Answer:

She should make the roped-off section 4 meters long and 2 meters wide.

Explanation:

Given that a paleontologist has 12 meters of twine to rope off a rectangular section,

so if we take the length as 4 m and width as 2 m then we can get the greatest possible area,

so the area of the rectangular section is

area = length × breadth

= 4 m ×2 m

= 8 m^{2}

**Show and Grow**

Question 5.

Newton has 16 feet of wood to make a rectangular sandbox. How long and wide should he make the sandbox so it has the greatest possible area?

Answer:

The greatest possible area of the rectangular sandbox is 15 ft^{2}

Explanation:

As Newton has 16 feet of wood to make a rectangular sandbox,

so let the length be 5 ft and the wide be 3 ft to get the greatest possible area,

so the area of the rectangular sandbox is

area = length × breadth

= 5 ft × 3 ft

= 15 ft^{2}

The greatest possible area of the rectangular sandbox is 15 ft^{2}

Question 6.

**DIG DEEPER!**

You and Newton are building forts. You each have the same length of rope to make a rectangular perimeter for the forton the ground. Your roped-off section is shown. Newton’s section has a greater area than yours. Draw one way Newton could rope off his fort.

Descartes also builds a fort. He has the same length of rope as you to make a perimeter around his fort. Descartes’s roped-off section has a lesser area than yours. Draw one way Descartes could rope off his fort.

Answer:

Refer the below for detailed explanation.

Explanation:

The length of the rope is 7 ft

and the breadth of the rope is 3 ft

the perimeter is

p = 2(length+breadth)

= 2(7+3)

= 2(10)

= 20 ft.

The area of the rectangle is

area= length×breadth

= 7×3

= 21 square feet.

Let the length of the Newton’s rope is 6 ft

and the breadth of the Newton’s rope is 4 ft

the perimeter is

p = 2(length+breadth)

= 2(6+4)

= 2(10)

= 20 ft.

The area of the rectangle is

area= length×breadth

= 6×4

= 24 square feet.

And here Newton’s area is greater.

Let the length of the Descarte’s rope is 8 ft

and the breadth of the Descarte’s rope is 2 ft

the perimeter is

p = 2(length+breadth)

= 2(8+2)

= 2(10)

= 20 ft.

The area of the rectangle is

area= length×breadth

= 8×2

= 16 square feet.

And here Descartes area is lesser.

### Same Perimeter, Different Areas Homework & Practice 15.4

Question 1.

Find the perimeter and the area of Rectangle A. Draw a different rectangle that has the same perimeter? Which rectangle has the greater area?

Perimeter = ___

Area = ___

Perimeter = ___

Area = ___

Rectangle __ has the greater area.

Answer:

The perimeter of the rectangle A is 7 cm

and the area of the rectangle A is 24 cm^{2}

The perimeter of rectangle B is 26 ft

and the area of the rectangle B is 30 ft2

The rectangle B has a greater area.

Explanation:

Given the length of the rectangle is 7 cm,

and the breadth of the rectangle is 5 cm,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(7 + 5)

= 2(12)

= 24 cm.

And the area of the rectangle is

a = length × breadth

= 7 × 5

= 35 cm^{2}.

we can see in the above figure rectangle with a length of 6.5 cm,

and the breadth is 5.5 cm,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(6.5 + 5.5)

= 2(12)

= 24 ft.

And the area of the rectangle is

area = length × breadth

= 6.5×5.5

= 35.75 square feet

So the rectangle B has a greater area.

Question 2.

**Patterns**

Complete the pattern. Find the area of each rectangle.

Each rectangle has the same perimeter. As the area increases, what do you notice about the shape of the rectangle?

Answer:

As the area increases the shape of the figure was changed, we can see the figure was changed from rectangle to square.

Explanation:

As we know that the perimeter of the above figure is the same,

so the perimeter of the above figures is

p = 2 (length + breadth)

= 2 (1 m+9 m)

= 2(10 m)

= 20 m.

So, the perimeter of the above figures is 20 m.

The area of figure 1 is

area = length × breadth

= 1 m × 9 m

= 9 m^{2}.

The area of figure 2 is

= 8m × 2m

= 16 m^{2}.

The area of figure 3 is

= 7m × 3m

= 21 m^{2}.

Let the length of figure 4 be 6m and the breadth be 4m,

The area of figure 4 is

= 6m × 4m

= 24 m^{2}.

Let the length of figure 5 be 5m and the breadth be 5m,

The area of figure 5 is

= 5m × 5m

= 25 m^{2}.

Question 3.

**Modeling Real Life**

You are making a card with a 36-centimeter ribbon border. How long and wide should you make the card so you have the greatest possible area to write?

Answer:

The length and the breadth of the card is 9 cm.

Explanation:

Given the perimeter of the card with a ribbon border is 36 cm

so the length of the card is

p =4a

36 = 4a

a= 36/4

= 9 cm.

The length and the breadth of the card is 9 cm.

The area of the card is

a = length×breadth

= 9×9

= 81 square cm.

Question 4.

**DIG DEEPER!**

A school has two rectangular playgrounds that each have the same perimeter. The first playground is shown. The second has a lesser area than the first. Draw one way the second playground could look.

The school builds another playground. It has the same perimeter as the ﬁrst. The third playground has a greater area than the ﬁrst. Draw one way the third playground could look

Answer:

Explanation:

**Review & Refresh**

Question 5.

2 × 30 = ___

Answer:

60

Explanation:

On multiplying 2 × 30 we will get 60.

Question 6.

6 × 20 = ___

Answer:

120

Explanation:

On multiplying 6 × 20 we will get 120.

Question 7.

3 × 90 = ___

Answer:

270

Explanation:

On multiplying 3 × 90 we will get 270.

### Lesson 15.5 Same Area, Different Perimeters

**Explore and Grow**

Use color tiles to create two different rectangles that each have an area of 18 square units. Then draw your rectangles and label their dimensions. Do the rectangles have the same perimeter? Explain how you know

Answer:

By comparing the perimeters of both rectangles, we can see that the perimeters are not the same.

Explanation:

In the above figure, we can see two colored rectangles

the length of rectangle 1 is 6 units

and the breadth of rectangle 1 is 3 units

so the perimeter of rectangle 1 is

p = 2(length+breadth)

= 2(6+3)

= 2(9)

= 18 units

and the area of rectangle 1 is

area= length×breadth

= 6×3

= 18 square units

The length of rectangle 2 is 9 units

and the breadth of rectangle 2 is 2 units

so the perimeter of rectangle 2 is

p = 2(length+breadth)

= 2(9+2)

= 2(11)

= 22 units.

and the area of rectangle 2 is

area= length×breadth

= 9×2

= 18 square units.

By comparing the perimeters of both rectangles, we can see that the perimeters are not the same.

**Repeated Reasoning**

As the perimeter increases and the area stays the same, what do you notice about the shape of the rectangle?

Think and Grow : Same Area, Different Perimeters

Example

Find the area and the perimeter of Rectangle A. Draw a different rectangle that has the same area. Which rectangle has the lesser perimeter?

Area = 2 × 6

= _____

Perimeter = 6 + 2 + 6 + 2

= ______

Area = ___ × ___

= ____

Perimeter = ___ + ___ + ___ + ___

= ____

Rectangle ___ has the lesser perimeter.

Answer:

The perimeter of the rectangle A is 16 ft

and the area of the rectangle A is 12 ft^{2}

The perimeter of rectangle B is 14 ft

and the area of the rectangle B is 12 ft^{2}

The rectangle A has a lesser area.

Explanation:

Given the length of the rectangle is 6 ft,

and the breadth of the rectangle is 2 ft,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(6 + 2)

= 2(8)

= 16 ft.

And the area of the rectangle is

a = length × breadth

= 6 × 2

= 12 ft^{2}

we can see in the above figure rectangle B and the length be 4 ft,

and the breadth be 3ft,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(4 + 3)

= 2(7)

= 14 ft.

And the area of the rectangle is

area = length × breadth

= 4×3

= 12 ft^{2}

So the rectangle A has a lesser area.

**Show and Grow**

Question 1.

Find the area and the perimeter of Rectangle A. Draw a different rectangle that has the same area. Which rectangle has the lesser perimeter?

Area = ___

Perimeter = ___

Area = ___

Perimeter = ___

Rectangle __ has the lesser perimeter.

Answer:

The perimeter of the rectangle A is 16 ft

and the area of the rectangle A is 12 ft^{2}

The perimeter of rectangle B is 14 ft

and the area of the rectangle B is 12 ft^{2}

The rectangle A has a lesser area.

Explanation:

Given the length of the rectangle is 6 cm,

and the breadth of the rectangle is 6 cm,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(6 + 6)

= 2(12)

= 24 cm.

And the area of the rectangle is

a = length × breadth

= 6 × 6

= 36 cm^{2}

we can see in the above figure rectangle B and the length be 9 cm,

and the breadth be 4 cm,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(9 + 4)

= 2(13)

= 26 cm.

And the area of the rectangle is

area = length × breadth

= 9×4

= 36 cm^{2}

So the rectangle A has a lesser perimeter.

**Apply and Grow: Practice**

Find the area and the perimeter of Rectangle A. Drawa different rectangle that has the same area. Which rectangle has the lesser perimeter?

Answer:

Question 2.

Rectangle A

Area = ___

Perimeter = ___

Rectangle B

Area = ___

Perimeter = ___

Rectangle ___ has the lesser perimeter.

Answer:

The perimeter of the rectangle A is 24 in

and the area of the rectangle A is 20 in^{2}

The perimeter of rectangle B is 18 in

and the area of the rectangle B is 20 in^{2}

The rectangle B has a lesser perimeter.

Explanation:

Given the length of the rectangle is 10 in,

and the breadth of the rectangle is 2 in,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(10 + 2)

= 2(12)

= 24 in.

And the area of the rectangle is

a = length × breadth

= 10 × 2

= 20 in^{2}

we can see in the above figure rectangle B and the length be 5 in,

and the breadth be 4 in,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(5 + 4)

= 2(9)

= 18 in.

And the area of the rectangle is

area = length × breadth

= 5×4

= 20 in^{2}

So the rectangle B has a lesser perimeter.

Question 3.

Rectangle A

Area = ___

Perimeter = ___

Rectangle B

Area = ___

Perimeter = ___

Rectangle ___ has the lesser perimeter.

Answer:

The perimeter of the rectangle A is 12 m

and the area of the rectangle A is 8 m^{2}

The perimeter of rectangle B is 18 m

and the area of the rectangle B is 8 m^{2}

The rectangle A has a lesser perimeter.

Explanation:

Given the length of the rectangle is 4 m,

and the breadth of the rectangle is 2 m,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(4 + 2)

= 2(6)

= 12 m.

And the area of the rectangle is

a = length × breadth

= 4 × 2

= 8 m^{2}

we can see in the above figure rectangle B and the length be 8 m,

and the breadth be 1 m,

so the perimeter of the rectangle is

p = 2(length + breadth)

= 2(8+ 1)

= 2(9)

= 18 m.

And the area of the rectangle is

area = length × breadth

= 8×1

= 8 m^{2}

So the rectangle A has a lesser perimeter.

Question 4.

**DIG DEEPER!**

The perimeter of a blue rectangle is 10 feet. The perimeter of a green rectangle is 14 feet. Both rectangles have the same area. Find the area and the dimensions of each rectangle.

Answer:

Explanation:

Given the perimeter of the blue rectangle is 10 ft and

the perimeter of the green rectangle is 14 ft

**Think and Grow: Modeling Real Life**

You have 40 square patio bricks that are each 1 foot long and 1 foot wide. You want to make a rectangular patio with all of the bricks. How long and wide should you make the patio so it has the least possible perimeter?

Draw to show:

You should make the patio ___ feet long and ___ feet wide.

Answer:

You should make the patio 8 feet long and 5 feet wide.

The least possible perimeter is 26 feet.

Explanation:

As there are 40 square patio bricks and each brick is 1 foot long and 1 foot wide

so to make a rectangular patio we need

the length of the rectangular patio be 8 feet

and the breadth of the rectangular patio be 5 feet

so the perimeter of the rectangular patio is

p= 2(length+breadth)

= 2(8+5)

= 2(13)

= 26 feet.

The least possible perimeter is 26 feet.

**Show and Grow**

Question 5.

Your friend has 16 square foam tiles that are each 1 foot long and 1 foot wide. He wants to make a rectangular exercise space with all of the tiles. How long and wide should he make the exercise space so it has the least possible perimeter?

Answer:

The least possible perimeter is 16 feet.

Explanation:

As there are 16 square foam tiles and each foam tile is 1 foot long and 1 foot wide

so to make an exercise space we need

the length of the exercise space be 4 feet

and the breadth of the exercise space be 4 feet

so the perimeter of the exercise space is

p= 2(length+breadth)

= 2(4+4)

= 2(8)

= 16 feet.

The least possible perimeter is 16 feet.

Question 6.

**DIG DEEPER!**

You and your friend each use fencing to make a rectangular playpen for a puppy. Each pen has the same area. Your pen is shown. Your friend’s pen uses less fencing than yours. Draw one way your friend could make her pen.

Your cousin makes a playpen for a puppy. His pen has the same area as your pen. Your cousin’s pen uses more fencing than yours. Draw one way your cousin could make his pen.

Answer:

### Same Area, Different Perimeters Homework & Practice 15.5

Question 1.

Find the area and the perimeter of Rectangle A. Drawa different rectangle that has the same area. Which rectangle has the lesser perimeter?

Area = ___

Perimeter = ___

Area = ___

Perimeter = ___

Rectangle __ has the lesser perimeter.

Answer:

The perimeter of rectangle A is 4 in

and the area of rectangle A is 20 square inches.

It is not possible to draw a rectangle that has the same area and different perimeter.

Explanation:

Given the length of the rectangle is 4 in,

and the breadth of the rectangle is 4 in,

so the perimeter of the rectangle is

p = 2( length + breadth)

= 2(4+4)

= 2(8)

= 16 in.

And the area of the rectangle is

a = length × breadth

= 4 × 4

= 16 square inches.

Question 2.

**Structure**

The dimensions of a rectangle are 4 feet by 10 feet. Which shape has the same area, but a different perimeter?

Answer:

The yellow shape rectangle has the same area and different perimeter.

Explanation:

Given the dimensions of the rectangle are 4 feet by 10 feet

so the perimeter of the rectangle is

p= 2(length+breadth)

= 2(4+10)

= 2(14)

= 28 feet.

The area of the rectangle is

area = length×breadth

= 10×4

= 40 square feet.

Here, we can see the yellow rectangle has a length of 8 feet

and the breadth of the rectangle is 5 feet

so the perimeter of the rectangle is

p = 2(length+beadth)

= 2(8+5)

= 2(13)

= 26 feet.

and the area of the rectangle is

area = length×breadth

= 8×5

= 40 square feet.

Question 3.

MP Reasoning

The two ﬁelds have the same area. Players run one lap around each ﬁeld. At which ﬁeld do the players run farther?

Answer:

As the perimeter of field A is greater than field B so in field A the players run father.

Explanation:

Let the length of field A is 10m

and the breadth of field A is 2m

so the perimeter of field A is

p = 2(length+breadth)

= 2(10+2)

= 2(12)

= 24 m.

and the area of field A is

area= length×breadth

= 10×2

= 20 square meters.

Let the length of field B is 5m

and the breadth of field B is 4m

so the perimeter of field B is

p = 2(length+breadth)

= 2(5+4)

= 2(9)

= 18 m.

and the area of field A is

area= length×breadth

= 5×4

= 20 square meters.

As the perimeter of field A is greater than field B so in field A the players run father.

Question 4.

**Modeling Real Life**

You have 24 square pieces of T-shirt that are each 1 foot long and 1 foot wide. You want to make a rectangular T-shirt quilt with all of the pieces. How long and wide should you make the quilt so it has the least possible perimeter?

Answer:

The least possible perimeter is 20 feet.

Explanation:

As there are 24 square pieces of T-shirt and each was 1 foot long and 1 foot wide

so to make a rectangular T-shirt quilt with all of the pieces we need

the length of the rectangular T-shirt quilt be 6 feet

and the breadth of the rectangular T-shirt quilt be 4 feet

so the perimeter of the rectangular T-shirt quilt is

p= 2(length+breadth)

= 2(6+4)

= 2(10)

= 20 feet.

The least possible perimeter is 20 feet.

Question 5.

**DIG DEEPER!**

You and Descartes each have40 cobblestone tiles to arrange in to a rectangular pathway. Your pathway is shown. Descartes’s pathway has a lesser perimeter than yours. Draw one way Descartes could make his pathway.

Newton also makes a rectangular pathway with 40 cobblestone tiles. His pathway has a greater perimeter than yours. Draw one way Newton could make his pathway.

Answer:

**Review & Refresh**

Identify the number of right angles and pairs of parallel sides.

Question 6.

Right angles: ___

Pairs of Parallel sides: ___

Answer:

Right angles: 1

Pairs of Parallel sides: 2.

Explanation:

In the above figure, we can see there are the right angle is 1, and the pairs of parallel sides are 2.

Question 7.

Right angles: ___

Pairs of parallel sides: ____

Answer:

Right angles: 4.

Pairs of Parallel sides: 2.

Explanation:

In the above figure, we can see there are the right angle is 4, and the pairs of parallel sides are 2.

### Find Perimeter and Area Performance Task

You and your cousin build a tree house.

Question 1.

The ﬂoor of the tree house is in the shape of a quadrilateral with parallel sides that are 4 feet long and 10 feet long. The other 2 sides are equal in length. The perimeter is 24 feet. Sketch the ﬂoor and label all of the side lengths.

Answer:

The length of the sides is 6 feet.

Explanation:

The perimeter of the floor is 24 feet

so the length of the floor be 6 feet

as the two other sides are also equal

so the other side length also be 6 feet

and let’s check the perimeter

p = 2(length+breadth)

= 2(6+6)

= 2(12)

= 24 feet.

Question 2.

Each rectangular wall of the tree house is 5 feet tall. How many square feet of wood is needed for all of the walls?

Answer:

Explanation:

Question 3.

You cut out a door in the shape of a rectangle with sides that are whole numbers. Its area is 8 square feet. What is the height of the door?

Answer:

The height of the rectangular door is 4 feet.

Explanation:

The area of the rectangular shape door is 8 square feet

as the sides of the rectangular door are whole numbers

so the length rectangular door be 4 feet

and the breadth be 2 feet

then we can get the area 8 square feet

let’s check the area

area = length×breadth

= 4×2

= 8 square feet.

So the height of the rectangular door is 4 feet.

Question 4.

You want to paint the ﬂoor and walls on the inside of your tree house. The area of the ﬂoor is 28 square feet. Each quart of paint covers 100 square feet.

a. How many quarts of paint do you need to buy?

b. Do you have enough paint to paint the outside walls of the tree house? Explain.

Answer:

a. 2,800 square feet quarts of paint we need to buy.

Explanation:

a. The area of the ﬂoor is 28 square feet and each quart of paint covers 100 square feet, so we need to buy

28×100= 2,800 square feet quarts of paint.

b.

### Find Perimeter and Area Activity

**Perimeter Roll and Conquer**

Directions:

1. Players take turns rolling two dice.

2. On your turn, draw a rectangle on the board using the numbers on the dice as the side lengths. Your rectangle cannot cover another rectangle.

3. Write an equation toﬁnd the perimeter of the rectangle.

4. If you cannot ﬁt a rectangle on the board, then you lose your turn. Play 10 rounds, if possible.

5. Add all of your rectangles’ perimeters together. The player with the greatest sum wins!

Answer:

Explanation:

### Find Perimeter and Area Chapter Practice

**15.1 Understand Perimeter**

Find the perimeter of the figure

Question 1.

Perimeter = ___

Answer:

The perimeter of the rectangle is 18 cm.

Explanation:

In the above figure, we can see the rectangle

with a length of 5 cm,

and the breadth of 4 cm

the perimeter of the rectangle is

p = 2 (length + breadth)

= 2 (5+4)

= 2(9)

= 18 cm.

Question 2.

Perimeter = ___

Answer:

The perimeter of the figure is 26 ft.

Explanation:

To find the perimeter of the above figure,

we will add the lengths of all sides of the figure

the sides of the above figure is 2 ft, 8 ft, 3 ft, 2 ft, 2 ft, 2 ft, 1 ft, 1 ft, 2 ft, 3 ft

the perimeter of the above figure is

p = 2+8+3+2+2+2+1+1+2+3

= 26 ft.

Question 3.

Draw a figure that has a perimeter of 10 inches.

Answer:

**15.2 Find Perimeter of Polygons**

Find the perimeter of the polygon

Question 4.

Perimeter = ___

Answer:

The perimeter of the polygon is 33 cm.

Explanation:

To find the perimeter of the polygon, we will add all the sides of the polygon

so the sides of the polygon are 9 cm, 6 cm, 8 cm, 10 cm

the perimeter of the polygon is

p = 9 cm +6 cm +8 cm +10 cm

= 33 cm.

Question 5.

Perimeter = ___

Answer:

The perimeter of the figure is 27 ft.

Explanation:

To find the perimeter of the figure, we will add all the sides of the figure

so the sides of the perimeter is 5 ft, 11 ft, 7 ft, 3 ft, 1 ft

the perimeter of the figure is

p = 5 ft+11 ft+ 7 ft+3 ft+1 ft

= 27 ft.

Question 6.

Parallelogram

Perimeter = ___

Answer:

The perimeter of the parallelogram is 12 m.

Explanation:

Given the length of the parallelogram is 4 m

and the breadth of the parallelogram is 2 m

the perimeter of the parallelogram is

p = 2 (length + breadth)

= 2( 4 m+ 2 m)

= 2(6 m)

= 12 m

Find the perimeter of the polygon

Question 7.

Rhombus

Perimeter = ___

Answer:

The perimeter of the rhombus is 36 cm.

Explanation:

Given the length of the side of the rhombus is 9 cm

and the perimeter of the rhombus is

p = 4a

= 4× 9 cm

= 36 cm.

Question 8.

Rectangle

Perimeter = ___

Answer:

The perimeter of the rectangle is 26 in.

Explanation:

The length of the rectangle is 5 inch

and the breadth of the rectangle is 8 inch

the perimeter of the rectangle is

p = 2( length + breadth)

= 2( 5 in+ 8 in)

= 2(13 in)

= 26 in.

So the perimeter of the rectangle is 26 in.

Question 9.

Square

Perimeter = ___

Answer:

The perimeter of the square is 28 ft.

Explanation:

The length of the square is 7 ft

so the perimeter of the square is

perimeter= 4a

= 4×7

= 28 ft.

Question 10.

**Modeling Real Life **

You want to put lace around the tops of the two rectangular lampshades. How many centimeters of lace do you need?

Answer:

We need 1,120 square centimeters.

Explanation:

The length of the rectangular lampshades is 35 cm

The breadth of the rectangular lampshades is 32 cm

and the area of the rectangular lampshades is

area= length×breadth

= 32×35

= 1,120 square cm.

So 1,120 square centimeters of lace you need.

**15.3 Find Unknown Side Lengths**

Find the unknown side length.

Question 11.

Perimeter = 22 feet

d = ____

Answer:

The length of the other side is 9 ft.

Explanation:

Given the perimeter of the above figure is 22 feet

and the length of the sides of the figure is 6 ft, 7 ft, d ft

so the perimeter of the figure is

p = 6 ft+ 7 ft+ d ft

22 ft = 13 ft + d ft

d = 22 ft – 13 ft

= 9 ft.

So, the length of the other side is 9 ft.

Question 12.

Perimeter = 31 inches

k = ___

Answer:

The length of the other side is 5 in.

Explanation:

Given the perimeter of the above figure is 31 inches

and the length of the sides of the figure is 10 in, 4 in, 12 in and k in.

so the perimeter of the figure is

p = 10 in+ 4 in+ 12 in+k in

31 in = 26 in + k in

k = 31 in – 26 in

= 5 in.

So, the length of the other side is 5 in.

Question 13.

Perimeter = 34 meters

y = ___

Answer:

The length of the other side is 7 m.

Explanation:

Given the perimeter of the above figure is 34 meters

and the length of the sides of the figure is 11 m, 8 m, 2 m, 1 m, 5 m, y m.

so the perimeter of the figure is

p = 11 m+ 8 m+ 2 m+ 1 m+ 5 m+ y m

34 m = 27 m + y m

y = 34 m – 27 m

= 7 m.

So, the length of the other side is 7 m.

Find the unknown side length.

Question 14.

Perimeter = 24 feet

k = ___

Answer:

The length of the sides of the triangle is 8 feet.

Explanation:

The perimeter of the triangle is 24 feet

and the perimeter of the triangle is

p = 3a

24 feet = 3a

a= 24/3

= 8 feet.

So, the length of the sides of the triangle is 8 feet.

Question 15.

Perimeter = 16 meters

y = ___

Answer:

The length of the sides of the square is 4 meters.

Explanation:

The perimeter of the triangle is 16 meters

and the perimeter of the triangle is

p = 4a

16 meters = 4a

a= 16/4

= 4 meters.

So, the length of the sides of the triangle is 4 meters.

Question 16.

Perimeter = 30 inches

d = ___

Answer:

The length of the sides of the pentagon is 6 inches.

Explanation:

The perimeter of the pentagon is 30 inches

and the perimeter of the pentagon is

p = 5a

30 inches = 5a

d= 30/5

= 6 inches.

So, the length of the sides of the pentagon is 6 inches.

Question 17.

**Number Sense**

A rectangle has a perimeter of 38 centimeters. The left side length is 10 centimeters. What is the length of the top side?

Answer:

The length of the top side is 9 cm.

Explanation:

Given the perimeter of the rectangle is 38 cm and

the left side length is 10 cm

Let the length of the top side be X, so

perimeter of the rectangle is

p = 2( length +breadth)

38 = 2(10+X)

38/2 = 10 + X

19 = 10 + X

X = 19 – 10

= 9 cm.

So the length of the top side is 9 cm.

**15.4 Same Perimeter, Different Area**

Question 18.

Find the perimeter and area of Rectangle A. Drawa different rectangle that has the same perimeter. Which rectangle has the greater area?

Perimeter = ____

Area = ___

Perimeter = ____

Area = ___

Rectangle ___ has the greater area.

Answer:

The perimeter of the rectangle A is 14 m

The area of the rectangle A is 10 square meters

The perimeter of the rectangle B is 14 m

The area of the rectangle B is 12 square meters

The rectangle B has greater area.

Explanation:

The length of the rectangle is 5m

and the breadth of the rectangle is 2m

the perimeter of the rectangle is

p= 2(length+breadth)

= 2(5+2)

= 2(7)

= 14 m

and the area of the rectangle is

area = length×breadth

= 2×5

= 10 square meters.

In the above image, we can see the length of the rectangle is 4 m

and the breadth of the rectangle is 3 m

so the perimeter of the rectangle is

p= 2(length+breadth)

= 2(4+3)

= 2(7)

= 14 m.

and the area of the rectangle is

area = length×breadth

= 4×3

= 12 square meters.

The rectangle B has greater area.

Question 19.

**Patterns**

Each Rectangle has the same perimeter. Are the areas increasing or decreasing ? Explain.

Answer:

As we can see in the above images the length of the images was increasing one by one and the breadth is decreasing, so the areas increasing or decreasing will depend upon the breadth of the rectangle. So, if the breadth is also increasing then the area will also be increasing. And if the breadth was decreasing then the area will also be decreasing.

**15.5 Same Area, Different Perimeters**

Question 20.

Find the area and the perimeter of Rectangle A. Drawa different rectangle that has the same area. Which rectangle has the lesser perimeter?

Area = ___

Perimeter = ___

Area = ___

Perimeter = ___

Rectangle ___ has the lesser perimeter.

Answer:

The perimeter of the rectangle A is 14 m

The area of the rectangle A is 10 square meters

The perimeter of the rectangle B is 14 m

The area of the rectangle B is 12 square meters

The rectangle B has greater area.

Explanation:

The length of the rectangle is 10 in

and the breadth of the rectangle is 5 in

the perimeter of the rectangle is

p= 2(length+breadth)

= 2(10+5)

= 2(15)

= 30 in

and the area of the rectangle is

area = length×breadth

= 10×5

= 50 square inches.

Question 21.

**Reasoning**

The two dirt-bike parks have the same area. Kids ride dirt bikes around the outside of each park. At which park do the kids ride farther ? Explain.

Answer:

As the length of the park B is longer, so at the park B kids rid farther than the park A.

### Find Perimeter and Area Cumulative practice 1 – 15

Question 1.

A mango has a mass that is 369 grams greater than the apple. What is the mass of the mango?

A. 471 grams

B. 369 grams

C. 267 grams

D. 461 grams

Answer:

B.

Explanation:

The mass of the mango is 369 grams greater than apple

Question 2.

Which term describes two of the shapes shown, but all three of the shapes?

A. polygon

B. rectangle

C. square

D. parallelogram

Answer:

B, C, D.

Explanation:

In the above figures, we can see the parallelogram and the square. As the square is also known as a rectangle so we will choose option B also.

Question 3.

A rectangular note card has an area of 35 square inches. The length of one of its sides is 7 inches. What is the perimeter of the note card?

A. 5 inches

B. 24 inches

C. 84 inches

D. 12 inches

Answer:

The breadth of the rectangular note card is 24 inches.

Explanation:

The area of the rectangular note card is 35 square inches and the length of one of its sides is 7 inches

so the breadth of the rectangular note card is

area = length × breadth

35 = 7 × breadth

breadth = 35/7

= 5 inches.

The perimeter of the rectangular note card is

p = 2(length+breadth)

= 2(7+5)

= 2(12)

= 24 inches.

The breadth of the rectangular note card is 24 inches.

Question 4.

How many minutes are equivalent to4 hours?

A. 400 minutes

B. 240 minutes

C. 24 minutes

D. 40 minutes

Answer:

B

Explanation:

The number of minutes is equivalent to 4 hours is

4× 60= 240 minutes.

Question 5.

A balloon artist has 108 balloons. He has 72 white balloons, and an equal number of red, blue, green, and purple balloons. How many purple balloons does he have?

A. 36

B. 180

C. 9

D. 32

Answer:

9 balloons.

Explanation:

As a balloon artist has 108 balloons and he has 72 white balloons

and the remaining balloons are 108 – 72= 36 balloons

and an equal number of red, blue, green, and purple balloons

which means 36 balloons are equally divided by 4 colors of balloons, so

36÷4 = 9 balloons.

So the purple balloons are 9.

Question 6.

Which statements about the figures are true?

Answer:

The shapes have different perimeters.

The shapes have the same area.

Explanation:

The length of the side of the square is 6 in,

and the perimeter of the square is

p = 4a

= 4×6 in

= 24 in

The area of the square is a^2

= 6 in×6 in

36 in^2.

Question 7.

The graph show many students ordered each lunch option.

Part A How many students ordered lunch?

Part B Choose a lesser value for the key. How will the graph change?

Answer:

Part A: 60 students ordered lunch.

Part B: Turkey hot dog has a lesser value.

Explanation:

Part A:

The number of students who ordered lunch is

the grilled chicken was ordered by 21 students

Turkey hot dog was ordered by 9 students

A peanut butter and jelly sandwich was ordered by 12 students

the salad bar was ordered by 18 students

so the number of students who ordered lunch is

21+9+12+18= 60 students.

Part B:

The turkey hot dog was ordered by 9 students which is a lesser value.

Question 8.

Find the sum

Answer:

935

Explanation:

The sum of the above given numbers is 935

Question 9.

What is the perimeter of the figure?

A. 26 units

B. 22 units

C. 20 units

D. 16 unit

Answer:

B

Explanation:

The sides of the figure is 2,4,1,2,1,1,2,2,1,1,2,1,1,1

and the perimeter of the figure is

p = 2+4+1+2+1+1+2+2+1+1+2+1+1+1

= 22 units.

Question 10.

Which bar graph correctly shows the data?

Answer:

Graph B.

Explanation:

Graph B shows the correct graph data.

Question 11.

Which polygons have at least one pair of parallel sides?

Answer:

Red color polygon.

Explanation:

The red color polygon has one pair of parallel sides, as it is a trapezoid.

Question 12.

The perimeter of the polygon is 50 yards. What is the missing side length?

A. 41 yards

B. 10 yards

C. 91 yards

D. 9 yards

Answer:

The missing side length is 9 yards.

Explanation:

Given the perimeter of the polygon is 50 yards

Let the missing side length be X yd

and the lengths of the sides of the polygon is 15 yds, 6 yds, 13 yds, 7 yds, and X yd,

So the perimeter of the polygon is

p = 15 yd+6 yd+13 yd+ 7 yd+ X yd

50 yards = 41 yards + X Yards

X = 9 yards.

So the missing side length is 9 yards.

Question 13.

Which line plot correctly shows the data?

Answer:

A

Explanation:

Option A line plot shows the correct data.

Question 14.

Your friend is asked to draw a quadrilateral with four right angles. She says it can only be a square. Is she correct?

A. Yes, there is no other shape it can be.

B. No, it could also be a rectangle.

C. No, it could also be a hexagon.

D. No, it could also be a trapezoid.

Answer:

Yes, there is no other shape it can be.

Explanation:

Yes, she is correct. There is no other shape than the square with four right angles.

Question 15.

Which numbers round to480 when rounded to the nearest ten?

Answer:

484, 480, 478

Explanation:

The numbers that are rounded to 480 to the nearest ten is 484, 480, 478.

### Find Perimeter and Area Cumulative Steam Performance Task 1 – 15

Question 1.

Use the Internet or some other resource to learn more about crested geckos.

a. Write three interesting facts about geckos.

b. Geckos need to drink water every day. Is this amount of water milliliters or liters? Explain.

c. Geckos can live in a terrarium. Is the capacity of this terrarium milliliters liters measured in or?

Answer:

a) The three interesting facts about geckos are:

i) Geckos are a type of lizards and their toes help them to stick to any surface except Teflon.

ii) Gecko’s eyes are 350 times more sensitive than human eyes to light.

iii) Some of the pieces of Geckos have no legs and look more like snakes.

b) The number of water Geckos will have is in milliliters only as Geckos will not often drink water.

c)Yes, geckos can live in a terrarium and the capacity of this terrarium is between 120 liters to 200 liters.

Question 2.

Your class designs a terrarium for a gecko.

a. The base of the terrarium is a hexagon. Each side of the hexagon is 6 inches long. What is the perimeter of the base?

b. The terrarium is 20 inches tall. All of the side walls are made of glass. How many square inches of glass is needed for the terrarium?

c. Another class designs a terrarium with a rectangular base. All of its sides are equal in length. The base has the same perimeter as the base your class designs. What is the perimeter of the base? What is the area?

Answer:

a. 36 inches.

b.

Explanation:

a.

Given the length of the sides of the hexagon is 6 inches, and

the perimeter of the hexagon is

p = 6a

= 6 × 6

= 36 inches.

Question 3.

An online store sells crested geckos. The store owner measures the length of each gecko in the store. The results are shown in the table.

a. Use the table to complete the line plot.

b. How many geckos did the store owner measure?

c. What is the difference in the lengths of the longest gecko and the shortest gecko?

d. How many geckos are shorter than 6\(\frac{1}{4}\) inches?

e.The length of a gecko’s tail is about 3 inches. How would the line plot change if the store owner measured the length of each gecko without its tail?

Answer:

b. The number of geckos the store owner measures is 24.

d. 12

Explanation:

a.

b. The number of geckos the store owner measures is 24.

d. The number of geckos shorter than 6\(\frac{1}{4}\) inches are 12.