## Everyday Mathematics 6th Grade Answer Key Unit 5 Area and Volume Explorations

### Everyday Mathematics Grade 6 Home Link 5.1 Answers

**Polygon Side Lengths**

Question 1.

Find any missing coordinates. Plot and label the points on the coordinate grid. Draw the polygon by connecting the points.

a. Rectangle ABCD

A: (1, 1) B: (-1, 1)

The length of \(\overline{B C}\) is represented by

|1| + |-4| = _______.

C: (_______, _______)

D: (_______, _______)

Answer:

b. Right triangle XYZ

X: (-5, 1) Z: (-3, 6)

The length of \(\overline{Z Y}\) is represented by |6| – |1| = _______.

The length of \(\overline{X Y}\) is represented by |-5| – |-3| = _______.

Y: (_______, _______)

Answer:

Question 2.

Use rectangle ABCD and triangle XYZ to fill in the following tables. The first row has been done as an example.

Answer:

**Practice**

Divide.

Write any remainders using R.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

### Everyday Math Grade 6 Home Link 5.2 Answer Key

**Finding the Areas of Parallelograms**

Find the area of each parallelogram. Show your work.

Question 1.

Area: ___________

Answer:

Question 2.

Area: ___________

Answer:

Question 3.

Area: ___________

Answer:

Question 4.

Area: ___________

Answer:

**Try This**

The area of each parallelogram is given. Find the length of each base.

Question 5.

Area: 26 square inches

Base: ___________

Answer:

Question 6.

Area: 5,015 square meters

Base: ___________

Answer:

**Practice**

Evaluate.

Question 7.

20% of 45 ________

Answer:

Question 8.

45% of 60 ________

Answer:

Question 9.

83% of 110 ________

Answer:

### Everyday Mathematics Grade 6 Home Link 5.3 Answers

**Triangle Area**

Find the area of each triangle. Remember: A = \(\frac{1}{2}\)bh.

Question 1.

Number model: _________

Area = _________

Answer:

Question 2.

Number model: _________

Area = _________

Answer:

Question 3.

Number model: _________

Area = _________

Answer:

Question 4.

Number model: _________

Area = _________

Answer:

Question 5.

Find the length of the base.

Area = 18 in.^{2}

Base = _________

Answer:

**Try This**

Question 6.

Draw a height for the triangle. Find the length of the height.

Area = 48 m^{2}

Height = _________

Answer:

**Practice**

Compute.

Question 7.

|-7| = ____

Answer:

Question 8.

|4| = ____

Answer:

Question 9.

______ = |-3|

Answer:

### Everyday Math Grade 6 Home Link 5.4 Answer Key

**Areas of Complex Shapes**

In Problems 1–4, decompose the shapes into polygons for which area formulas can be used. Label the areas. Find the total area for each shape. Use appropriate units.

Question 1.

Area: ________

Answer:

Question 2.

Area: ________

Answer:

Question 3.

Area: ________

Answer:

**Try This**

Question 4.

Area: ________

Answer:

**Practice**

Calculate.

Question 5.

12 – 8.25 = ________

Answer:

Question 6.

_______ = 9.03 + 0.7 + 18

Answer:

Question 7.

125.29 – 16.7 = ______

Answer:

Question 8.

_______ = 0.01 + 0.99

Answer:

### Everyday Mathematics Grade 6 Home Link 5.5 Answers

**Real- World Nets**

Circle the solid that can be made from each net.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Use the net and its corresponding geometric solid in Problem 2.

a. Which polygons make up the faces of your solid? How many are there of each kind? __________

b. Which faces are parallel? __________

c. Which faces are congruent? __________

d. How many edges are there? How many vertices? __________

Answer:

**Practice**

Multiply.

Question 4.

5.2 ∗ 3 = ______

Answer:

Question 5.

1.04 ∗ 2 = ______

Answer:

Question 6.

______ = 0.14 ∗ 3

Answer:

### Everyday Math Grade 6 Home Link 5.6 Answer Key

**Surface Area Using Nets**

Silly Socks is trying to choose a type of plastic box for their socks. The nets for three different box designs are given below.

Question 1.

Without calculating, predict which design will require the least amount of plastic to produce.

Answer:

Question 2.

Find the surface area for each plastic-box design. Write a number sentence to show how you found the surface area. Remember to use the correct order of operations.

Answer:

Question 3.

Explain how to find the surface area for any rectangular or triangular prism.

Answer:

**Practice**

Divide. Find your answer to the nearest hundredth.

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

### Everyday Mathematics Grade 6 Home Link 5.7 Answers

**Surface Area**

Question 1.

Sam is painting the outside of a doghouse dark green (except for the bottom, which is on the ground).

The doghouse measures 3 feet wide by 4.5 feet long. It is 4 feet high.

The roof is flat, so the doghouse looks like a rectangular prism.

The entrance to the dog house is 1.5 feet wide by 2 feet high.

a. Label the doghouse diagram with the measurements.

Answer:

b. On the grid below, draw a net for a prism that could represent Sam’s doghouse.

Scale: ☐ = 1 square foot

Answer:

c. How many square feet is he painting?

Answer:

d. One pint of paint covers about 44 ft^{2}. How many pints does he need?

Answer:

**Practice**

Evaluate.

Question 2.

4^{3} ______

Answer:

Question 3.

1.5^{2} _______

Answer:

Question 4.

1^{50} ______

Answer:

Question 5.

(\(\frac{2}{3}\))^{2} ______

Answer:

### Everyday Math Grade 6 Home Link 5.8 Answer Key

**Arguing about Areas**

Jayson was comparing the areas of the polygons at the right.

Here is Jayson’s reasoning: I think that Polygons K and L have the same area. I lined up the sides of each polygon and they were equal, so I labeled the sides with the same variables. So the area of Polygon K is equal to the area of Polygon L.

Question 1.

Explain the flaw in Jayson’s reasoning.

Answer:

Trace Polygon K above, and cut out your tracing. Use it to help you solve Problems 2–3.

Question 2.

Draw two different polygons that have the same area as PolygonK.

Answer:

Question 3.

Choose one of your polygons from Problem 2. Describe how you used Polygon K to draw a polygon that has the same area.

Answer:

For Lesson 5-9, bring a rectangular prism, such as an empty tissue box, to class.

**Practice**

Find the whole.

Question 4.

10% is 7, so 100% is ______.

Answer:

Question 5.

25% is 90, so 100% is _______.

Answer:

### Everyday Mathematics Grade 6 Home Link 5.9 Answers

**Volume of Rectangular Prisms**

Find the volume for each prism.

Question 1.

Volume ________

Answer:

Question 2.

Volume _______

Answer:

Question 3.

The Blueberry Blast cereal box is a rectangular prism that is 12 inches × 8 inches × 4 inches.

a. Label the diagram with the dimensions.

b. What is its volume?

Answer:

Question 4.

Greta’s gift shop has three sizes of gift boxes. They are all shaped like rectangular prisms. The dimensions are shown below.

Small: 10 cm × 10 cm × 10 cm

Large: 40 cm × 30 cm × 15 cm

Medium: The area of the base is 1,000 cm2 and the height is 8 cm.

Find the volume of each gift box

Small: ________

Large: ________

Medium: ________

Answer:

**Practice**

Evaluate

Question 5.

\(\frac{2}{3}\) + \(\frac{5}{6}\) = ________

Answer:

Question 6.

4\(\frac{3}{4}\) + \(\frac{7}{8}\) = _________

Answer:

Question 7.

\(\frac{4}{5}\) – \(\frac{3}{4}\) = _________

Answer:

Question 8.

10 – \(\frac{5}{12}\) = __________

Answer:

### Everyday Math Grade 6 Home Link 5.10 Answer Key

**Calculating Luggage Volume**

You may want to consider how much volume your luggage holds when you travel. If you know how to calculate the area of a rectangular prism, you can also find the approximate volume of a suitcase. Below are the measurements of some common suitcase sizes.

Question 1.

a. Find the volume of each suitcase.

Answer:

b. Find the approximate volume of the interiors. Round to the nearest 0.01 in.^{3}.

Answer:

Suitcase 1

Exterior: 17″ × 15″ × 8″

a. Volume: __________

Interior: 16″ × 13.75″ × 6.5″

b. Volume:__________

Suitcase 2

Exterior: 21″ × 14″ × 7″

a. Volume: __________

Interior: 19.5″ × 13″ × 5.75″

b. Volume: __________

Suitcase 3

Exterior: 24″ × 16″ × 9.75″

a. Volume: __________

Interior: 22.5″ × 14.75″ × 8.25″

b. Volume: __________

Suitcase 4

Exterior: 28″ × 19″ × 9″

a. Volume: __________

Interior: 26″ × 17.5″ × 7.5″

b. Volume: __________

Question 2.

Describe how you can estimate the interior volume of a suitcase if you know the exterior measurements.

Answer:

**Practice**

Evaluate.

Question 3.

\(\frac{2}{3}\) ÷ \(\frac{1}{6}\) = ________

Answer:

Question 4.

\(\frac{5}{12}\) ÷ \(\frac{7}{12}\) = _________

Answer:

Question 5.

_________ = 2\(\frac{2}{3}\) ÷ \(\frac{1}{2}\)

Answer:

Question 6.

8 ÷ 2\(\frac{2}{3}\) = ____________

Answer:

### Everyday Mathematics Grade 6 Home Link 5.11 Answers

**Volume of Letters**

The Santiago Balloon Emporium sells custom balloons shaped like letters of the alphabet. Clarissa orders balloons that spell DOLLIE for her friend’s birthday. She wants the balloons to float, so she plans to fill them with helium. To estimate how much it will cost, Clarissa needs to calculate the approximate volume of helium she will need to fill the balloons.

The volume of each balloon can be estimated based on rectangular prisms.

Measure the dimensions in millimeters for each rectangular part of the letters.

Question 1.

The scale is 1 mm = 1 inch. Each letter has a depth of 5 inches. Estimate the volume of each letter.

D: _________ O: _________ L:_________

I: _________ E: _________

Answer:

Question 2.

What is the approximate total volume of helium (in cubic inches) needed to fill the letters?

Answer:

Question 3.

a. Helium comes in tanks that hold either 8.9 ft^{3}, which cost $19.99 each, or 14.9 ft^{3}, which cost $28.99 each. What is the least amount Clarissa can spend to fill her letters with helium? Hint: There are 1,728 in.3 in 1 ft^{3}.

Answer:

b. Explain how you found your answer to Part a.

Answer:

**Practice**

Divide.

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

### Everyday Math Grade 6 Home Link 5.12 Answer Key

**Could a Giant Breathe?**

Think about how area and volume change in relation to changes in linear measurements.

Question 1.

How many centimeters are in 1 meter? ____________

Answer:

Question 2.

How many square centimeters are in 1 square meter? ____________

Answer:

Question 3.

How many cubic centimeters are in 1 cubic meter? ____________

One cubic centimeter of water has a mass of about 1 gram.

Answer:

Question 4.

One cubic meter of water has a mass of:

____________ grams ____________ kilograms

Answer:

Question 5.

One kilogram has a weight equivalent to about 2.2 pounds.

One cubic meter of water weighs about how many pounds? ____________

Answer:

Oxygen enters your body through the surface area of your lungs.

Question 6.

A giant who is 10 times as tall as you would have lungs that provide ____________ as much oxygen as your lungs.

Answer:

Question 7.

If the surface area of the giant’s lungs were 100 times greater than yours, and if the giant required oxygen in the same proportions as a human, how do you know the giant would not have enough oxygen? Explain.

Answer:

**Try This**

Question 8.

Your lungs fit in a relatively small space inside your rib cage. Research how your lungs increase surface area to be able to supply all the oxygen you need.

Answer:

**Practice**

For Problems 9–10 , record the opposite of the number.

Question 9.

-7 _______

Answer:

Question 10.

0 ______

Answer:

Question 11.

The opposite of the opposite of -3 ________

Answer: