Name Class Date 8-7
Surface Area
Going Deeper
Essential question: How can you use nets to find surface areas?
A net is a two-dimensional pattern of shapes that can be folded into a
three-dimensional figure. The shapes in the net become the faces of the
three-dimensional figure.
video tutor
CC.6.G.4
1
EXPLORE
A
Copy the following nets on graph paper and cut them out along the blue lines.
Net A
One of these nets can be folded along the black lines to make a cube. Which net
will NOT make a cube?
B
Net B
See if you can find another net that can be folded into a cube.
Draw a net that you think will make a cube on your graph paper, and then
cut it out. Can you fold it into a cube?
C
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Nets of a Cube
Compare your results with several of your classmates. How many different
nets for a cube did you and your classmates find?
REFLECT
How do you know that each net cannot be folded into a cube without
actually cutting and folding it?
1a.
1b.
1c. What shapes will appear in a net for a rectangular prism that is not a cube?
How many of these shapes will there be?
Chapter 8
377
Lesson 7
The surface area of a three-dimensional figure is the sum of the areas of its faces.
A net can be helpful when finding surface area.
CC.6.G.4
2
EXPLORE
Surface Area of a Rectangular Prism
The gift wrap department of a store has specially sized
boxes to wrap sweaters. Use the box’s dimensions to
label the dimensions of the net. Then find the surface
area of the box.
3 inches
10 inches
15 inches
inches
inches
inches
inches
inches
inches
inches
Complete the table to find the surface area.
Face
Top
Base (in.)
Height (in.)
Area (​in​2​)
15
10
150
Bottom
Front
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Back
Right
Left
Total
square inches.
The surface area of the sweater box is
REFLECT
2a. How did you find the area of each face?
2b. If the box had been a cube, how would finding the surface area have been easier?
Chapter 8
378
Lesson 7
A pyramid is a three-dimensional figure whose base is a polygon and whose other
faces are all triangles. A pyramid is named by its base. A pyramid whose base is
a triangle is a triangular pyramid. A pyramid whose base is a square is a square
pyramid, and so on.
CC.6.G.4
3
EXPLORE
Surface Area of a Pyramid
Find the surface area of the pyramid.
A
How many faces does the pyramid have?
B
What polygon forms the base of the pyramid?
16 in.
What is the formula for the area of this polygon?
A=
16 in.
in.
C
What polygon forms each of the other faces?
What is the formula for the area of this polygon?
D
Complete the net by labeling its dimensions.
E
Complete the table to find the surface area.
Face
Base
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17 in.
Base (in.)
in.
in.
Height (in.)
Area (i​n​2​)
16
Triangle
Triangle
Triangle
Triangle
Total
The surface area of the pyramid is
square inches.
REFLECT
3a. What would have been a quicker way to find the combined areas of the triangles?
3b. Surface area is measured in square units. Why are square units used when working with a
three-dimensional figure?
Chapter 8
379
Lesson 7
pr a c t i c e
Identify the three-dimensional figure formed by each net.
1.
2.
Draw a net for each three-dimensional figure.
3.
4.
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Find the surface area of each figure.
6.
5.
20 in.
12 ft
8 ft
18 in.
20 ft
Chapter 8
square feet
380
16 in.
square inches
Lesson 7
Name Class 8-7
Date Name ________________________________________ Date __________________ Class __________________
Measurement
and Geometry
Additional
Practice
Chapter
Practice B: Surface Area
Find the surface area S of each prism.
1.
2.
________________________________________
________________________________________
Find the surface area S of each pyramid.
3.
4.
________________________________________
________________________________________
5. A rectangular box has no top. It is 6 inches long, 4 inches wide,
and 5 inches tall. What is the surface area of the box?
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_________________________________________________________________________________________
6. The surface area of a rectangular prism is 48 square feet.
The area of its front is 4 square feet, and the area of one side is
10 square feet. What is the area of the top of the prism?
_________________________________________________________________________________________
Chapter 8
381
Practice and Problem Solving
55
Holt McDougal Mathematics
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Name ________________________________________ Date __________________ Class __________________
Measurement
and Geometry
Problem
Solving
Chapter
Problem Solving: Surface Area
Write the correct answer.
1. Tara made fuzzy cubes to hang in
her car. Each side of the 2 cubes is
4 inches long. How much fuzzy
material did Tara use to make both
cubes?
2. The top of the Washington
Monument is a square pyramid
covered with white marble. Each
triangular face is 58 feet tall and 34
feet wide. About how many square
feet of marble covers the top of the
monument? (The base is hollow.)
________________________________________
________________________________________
3. The Parthenon, a famous temple in
Greece, is surrounded by large stone
columns. Each column is 10.4 meters
tall and has a diameter of 1.9 meters.
To the nearest whole square meter,
what is the surface area of each
column (not including the top and
bottom)?
4. The tablet that the Statue of Liberty
holds is 7.2 meters long, 4.1 meters
wide, and 0.6 meters thick. The tablet
is covered with thin copper sheeting. If
the tablet was freestanding, how
many square meters of copper
covers the statue’s tablet?
________________________________________
________________________________________
Circle the letter of the correct answer.
6. A glass triangular prism for a
telescope is 5.5 inches tall. Each side
of the triangular base is 4 inches long,
with a 3-inch height. How much glass
covers the surface of the prism?
F 6 in2
A 727,272 ft2
B 727,722 ft
G 12 in2
2
H 39 in2
C 727,727 ft2
D 772,272 ft
J 78 in2
2
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Chapter 8
55
382
Practice
Problem
Solving
Holtand
McDougal
Mathematics
© Houghton Mifflin Harcourt Publishing Company
5. The largest Egyptian pyramid is
called the Great Pyramid of Khufu.
It has a 756-foot square base and a
slant height of 481 feet. What is the
total surface area of the faces of the
Pyramid of Khufu?