# Everyday Math Grade 6 Answers Unit 5 Area and Volume Explorations

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

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: (_______, _______)

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: (_______, _______)

Question 2.
Use rectangle ABCD and triangle XYZ to fill in the following tables. The first row has been done as an example.

Practice
Divide.
Write any remainders using R.
Question 3.

Question 4.

Question 5.

Question 6.

Finding the Areas of Parallelograms
Find the area of each parallelogram. Show your work.
Question 1.

Area: ___________

Question 2.

Area: ___________

Question 3.

Area: ___________

Question 4.

Area: ___________

Try This
The area of each parallelogram is given. Find the length of each base.
Question 5.

Area: 26 square inches
Base: ___________

Question 6.

Area: 5,015 square meters
Base: ___________

Practice
Evaluate.
Question 7.
20% of 45 ________

Question 8.
45% of 60 ________

Question 9.
83% of 110 ________

Triangle Area
Find the area of each triangle. Remember: A = $$\frac{1}{2}$$bh.
Question 1.

Number model: _________
Area = _________

Question 2.

Number model: _________
Area = _________

Question 3.

Number model: _________
Area = _________

Question 4.

Number model: _________
Area = _________

Question 5.
Find the length of the base.

Area = 18 in.2
Base = _________

Try This
Question 6.
Draw a height for the triangle. Find the length of the height.

Area = 48 m2
Height = _________

Practice
Compute.
Question 7.
|-7| = ____

Question 8.
|4| = ____

Question 9.
______ = |-3|

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: ________

Question 2.

Area: ________

Question 3.

Area: ________

Try This
Question 4.

Area: ________

Practice
Calculate.
Question 5.
12 – 8.25 = ________

Question 6.
_______ = 9.03 + 0.7 + 18

Question 7.
125.29 – 16.7 = ______

Question 8.
_______ = 0.01 + 0.99

Real- World Nets
Circle the solid that can be made from each net.
Question 1.

Question 2.

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? __________

Practice
Multiply.
Question 4.
5.2 ∗ 3 = ______

Question 5.
1.04 ∗ 2 = ______

Question 6.
______ = 0.14 ∗ 3

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.

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.

Question 3.
Explain how to find the surface area for any rectangular or triangular prism.

Practice
Question 4.

Question 5.

Question 6.

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.

b. On the grid below, draw a net for a prism that could represent Sam’s doghouse.
Scale: ☐ = 1 square foot

c. How many square feet is he painting?

d. One pint of paint covers about 44 ft2. How many pints does he need?

Practice
Evaluate.
Question 2.
43 ______

Question 3.
1.52 _______

Question 4.
150 ______

Question 5.
($$\frac{2}{3}$$)2 ______

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.

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.

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.

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 ______.

Question 5.
25% is 90, so 100% is _______.

Volume of Rectangular Prisms
Find the volume for each prism.
Question 1.

Volume ________

Question 2.

Volume _______

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?

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: ________

Practice
Evaluate
Question 5.
$$\frac{2}{3}$$ + $$\frac{5}{6}$$ = ________

Question 6.
4$$\frac{3}{4}$$ + $$\frac{7}{8}$$ = _________

Question 7.
$$\frac{4}{5}$$ – $$\frac{3}{4}$$ = _________

Question 8.
10 – $$\frac{5}{12}$$ = __________

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.

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

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.

Practice
Evaluate.
Question 3.
$$\frac{2}{3}$$ ÷ $$\frac{1}{6}$$ = ________

Question 4.
$$\frac{5}{12}$$ ÷ $$\frac{7}{12}$$ = _________

Question 5.
_________ = 2$$\frac{2}{3}$$ ÷ $$\frac{1}{2}$$

Question 6.
8 ÷ 2$$\frac{2}{3}$$ = ____________

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: _________

Question 2.
What is the approximate total volume of helium (in cubic inches) needed to fill the letters?

Question 3.
a. Helium comes in tanks that hold either 8.9 ft3, which cost $19.99 each, or 14.9 ft3, 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 ft3.

Practice
Divide.
Question 4.

Question 5.

Question 6.

Question 7.

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? ____________

Question 2.
How many square centimeters are in 1 square meter? ____________

Question 3.
How many cubic centimeters are in 1 cubic meter? ____________
One cubic centimeter of water has a mass of about 1 gram.

Question 4.
One cubic meter of water has a mass of:
____________ grams ____________ kilograms

Question 5.
One kilogram has a weight equivalent to about 2.2 pounds.
One cubic meter of water weighs about how many pounds? ____________

Question 6.
A giant who is 10 times as tall as you would have lungs that provide ____________ as much oxygen as your lungs.

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.

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.

Practice
For Problems 9–10 , record the opposite of the number.
Question 9.
-7 _______