We included HMH Into Math Grade 3 Answer Key PDF Module 11 Lesson 5 Represent Rectangles with the Same Perimeter and Different Areas to make students experts in learning maths.
HMH Into Math Grade 3 Module 11 Lesson 4 Answer Key Represent Rectangles with the Same Perimeter and Different Areas
I Can use area to compare rectangles with the same perimeter.
Step It Out
Question 1.
An art store sells rectangular canvas in two different sizes, but both have a perimeter of 10 feet. Gina wants the canvas with the greater possible area. Which canvas should she buy?
A. Draw all the possible rectangles with a perimeter of 10 feet.
Answer:
p = 10 feet
10 = 2(l + w)
(l + w)= 5
Let us consider l = 2
w = 3
2 + 3 = 5
For another let us consider l = 3
and w = 2
B. Find the area of each rectangle. Write equations.
Think: I can multiply the number of unit squares in each row by the number of rows.
Answer:
Area = l x w
a = 3 x 2
a = 6
Area = l x w
a = 2 x 3
a = 6
The area of the both rectangles are same.
C. The greater area is ___________ .
Answer:
The area of the both rectangles are same.
D. What are the side lengths of the canvas that Gina should buy?
Answer:
She can buy any canvas as the area of the both rectangles are same.
Turn and Talk Compare your rectangles. Look at the difference between the length and width and the area of a rectangle. What do you notice?
Answer:
The lengths change from one rectangle to the another rectangle
and same width also changes.
but area remains same for both rectangles.
Question 2.
Fran buys rectangular clay tiles. The perimeter of each clay tile is 18 inches.
A. Draw all the different rectangles with a perimeter of 18 inches.
Answer:
p = 2(l + w)
18 = 2(l + w)
l + w = 9
let us consider l = 5
w = 4
5 + 4 = 9,
let us consider l = 4
w = 5.
4 + 5 = 9
let us consider l = 3
w = 6
3 + 6 = 9
let us consider l = 6
w = 3
6 + 3 = 9
B. Find the area of each rectangle. Write equations.
Answer:
1) l = 5; w = 4.
area = l x w
a = 5 x 4 = 20
2) l = 4; w = 5.
area = l x w
a = 4 x 5 = 20
3) l = 3; w = 6.
area = l x w
a = 3 x 6 = 18
4) l = 6; w = 3.
area = l x w
a = 6 x 3 = 18
C. What is the difference between the length and width for each rectangle? Write equations.
Answer:
The area of 1 and 2 are same
the area of 3 and 4 are same
But the length and width changes.
2) l = 4; w = 5.
area = l x w
a = 4 x 5 = 20
3) l = 3; w = 6.
area = l x w
a = 3 x 6 = 18
D. What are the side lengths of the rectangle with the least area? Explain the difference between the side lengths.
Answer:
the side lengths of the rectangle with the least area is l = 3
w = 6
and area = 18
Check Understanding
Question 1.
Find the perimeter and area. Circle the letter of the rectangle with the greatest area.
A.
Perimeter = _________ units
Area = __________ square units
Answer:
Perimeter = 12 units
Area = 5 square units
Explanation:
p = 2(l + w)
p = 2 (1 + 5)
p = 12
a = l x w
a = 1 x 5
a = 5
B.
Perimeter = _________ units
Area = __________ square units
Answer:
Perimeter = 12 units
Area = 8 square units
Explanation:
p = 2(l + w)
p = 2 x 6
p = 12
a = l x w
a = 2 x 4
a = 8
C.
Perimeter = _________ units
Area = __________ square units
Answer:
Perimeter = 12 units
Area = 9 square units
Explanation:
p = 4a
p = 4 x 3
p = 12
a = a x a
a = 3 x 3
a = 9
On Your Own
Question 2.
Art David and Hilary each have a sketch book. Compare the perimeters and the areas of the sketch books. Show your work.
How can you describe the perimeter and area comparisons?
Answer:
Explanation:
David and Hilary have the same perimeter but different area
p = 2(l + w)
a = l x w
Question 3.
Open-Ended Write a word problem about perimeter and area that you could represent with this visual model.
Answer:
perimeter: 26 inches.
Area: 40 inches.
Explanation:
p = 2 (l + w)
p = 2(5 + 8)
p = 2 x 13
p = 26
Area = l x w
a = 5 x 8
a = 40
Question 4.
Circle the letter of the rectangle that has a perimeter of 22 units and an area of 30 square units.
Answer:
all the 3 figures have area = 30
figure b has perimeter = 22
Explanation:
Figure A:
Perimeter: 26
Area: 30
p = 2(l + w)
p = 2 (3 +10)
p = 26
a = l x w
a = 3 x 10
a = 30
Figure B:
Perimeter: 22
Area: 30
p = 2(l + w)
p = 2 x 11
p = 22
a = l x w
a = 5 x 6
a = 30
Figure C:
Perimeter: 34
Area: 30
p = 2(l + w)
p = 2 x 17
p = 34
a = l x w
a = 2 x 15
a = 30
Question 5.
STEM A prism separates white light into a band of seven colors called a spectrum. Jason hangs a rectangular poster of a prism rainbow on his wall. The poster has a perimeter of 14 feet. Draw all the possible shapes of the poster.
What are the side lengths of the rectangle with the least area?
Answer:
Explanation:
p = 14
p = 2(l + w)
14 = 2(l + w)
l + w = 7
1) let us consider l = 3
w = 4;
3 + 4 = 7
p = 14
a = 12
2) let us consider l = 4
w = 3;
4 + 3 = 7
p = 14
a = 12
3) let us consider l = 2
w = 5;
2 + 5 = 7
p = 14
a = 10
4)let us consider l = 5
w = 2;
5 + 2 = 7
p = 14
a = 10
Question 6.
Draw a rectangle that has the same perimeter as the one shown, but with a greater area.
Answer:
Explanation:
perimeter = 2 (l + w)
p = 2 x 8
p = 16
Area = l x w
a = 3 x 5 = 15
So, the next rectangle perimeter must be 16 but area should be greater
p = 2(l + w)
16 = 2(l + w)
l + w = 8
let us consider l = 4
and w = 4
area = l x w
a = 4 x 4
a = 16
Question 7.
Reason Tre and Eliie both buy rectangular frames for photographs. Both frames have the same perimeter. The difference between the length and width of Tre’s frame is 2 inches. The difference between the length and width of Ellie’s frame is 6 inches. Which frame will hold the photograph with the greater area? Explain.
Answer:
Tre’s frame hold the photograph with the greater area
Explanation:
The difference between the length and width of Tre’s frame is 2 inches
Let us consider the length is 6 and width is 4
So area is 6 x 4 = 24
perimeter is 2(6+4) = 2(10) =20
The difference between the length and width of Ellie’s frame is 6 inches.
Let us consider the length is 8 and width is 2
So area is 8 x 2 = 16
perimeter is 2(8+2) = 2(10) =20