8.3 Surface Areas of Pyramids - Big Ideas Learning
8.3
Surface Areas of Pyramids
How can you use a net to find the surface
area of a pyramid?
1
ACTIVITY: Identifying Pyramids
Work with a partner. Label one of the faces as a base and the other as a
lateral face. Use the shape of the base to identify the pyramid.
b.
a.
Pyramid
2
Pyramid
ACTIVITY: Using a Net
Work with a partner.
a. Copy the net shown below onto grid paper.
b. Cut out the net and fold it to form a pyramid. What type of rectangle is
the base? Use this shape to name the pyramid.
c. Find the surface area of the pyramid.
COMMON
CORE
Geometry
In this lesson, you will
use nets to represent
pyramids.
find the surface area
of pyramids.
solve real-life problems.
Learning Standard
6.G.4
368
Chapter 8
Surface Area and Volume
3
ACTIVITY: Estimating the Surface Area of a Triangular Pyramid
Work with a partner. Label each face in the net of the triangular pyramid as a
base or a lateral face. Then estimate the surface area of the pyramid.
Math
Practice
Analyze Givens
What information is
given in the diagram?
How does this help
you estimate the
surface area of
the pyramid?
6
6
4
ACTIVITY: Finding the Surface Area of a Square Pyramid
Work with a partner. Draw a net for each square pyramid. Use the net to find
the surface area of the pyramid.
a.
b.
3
5
3
5
5. IN YOUR OWN WORDS How can you use a net to find the surface area of
a pyramid?
6. CONJECTURE Make a conjecture about the lateral faces of a pyramid when
the side lengths of the base have the same measure. Explain.
Use what you learned about the surface area of a pyramid to
complete Exercises 3C5 on page 372.
Section 8.3
Surface Areas of Pyramids
369
8.3
Lesson
Lesson Tutorials
Net of a Square Pyramid
A square pyramid is a pyramid with a square base.
side
Unfold.
side
Flatten.
bottom
side
base
EXAMPLE
1
side
Finding the Surface Area of a Square Pyramid
Find the surface area of the square pyramid.
10 m
Use a net to find the area of each face.
Bottom:
7m
Side:
Side:
Side:
Side:
?
? ?
1
? 7 ? 10 = 35
2
1
? 7 ? 10 = 35
2
1
? 7 ? 10 = 35
2
7 7 = 49
sides
1
7 10 = 35
2
7m
10 m
7 m bottom
sides
Find the sum of the areas of the faces.
Area of
Area of
Area of
Area of
Area of
Surface
+
+
+
+
=
bottom
a side
a side
a side
a side
Area
S
=
49
+
35
+
35
+
35
+
35
= 189
So, the surface area is 189 square meters.
Find the surface area of the square pyramid.
Exercises 6C8
1.
2.
3.
5 cm
3 ft
2 ft
370
Chapter 8
Surface Area and Volume
3.6 in.
5 cm
4 in.
Net of a Triangular Pyramid
A triangular pyramid is a pyramid with a triangular base.
Study Tip
side
The base of each
triangular pyramid
in this section is an
equilateral triangle.
Unfold.
Flatten.
bottom
side
side
base
EXAMPLE
2
Finding the Surface Area of a Triangular Pyramid
Find the surface area of the triangular pyramid.
Use a net to find the area of each face.
1
2
1
2
1
2
1
2
Bottom:
8 ft
5.2 ft
Side:
Side:
6 ft
Side:
? 6 ? 5.2 = 15.6
? 6 ? 8 = 24
? 6 ? 8 = 24
? 6 ? 8 = 24
5.2 ft
6 ft
8 ft
Find the sum of the areas of the faces.
Area of
Area of
Area of
Area of
Surface
+
+
+
=
bottom
a side
a side
a side
Area
S
=
15.6
+
24
+
24
+
24
= 87.6
So, the surface area is 87.6 square feet.
Find the surface area of the triangular pyramid.
Exercises 9C11
4.
5.
3 cm
7 in.
6.
7.8 in.
12 yd
17.3 yd
1.7 cm
9 in.
2 cm
Section 8.3
Surface Areas of Pyramids
20 yd
371
Exercises
8.3
Help with Homework
1. PRECISION Explain how to find the surface area of a pyramid.
2. WHICH ONE DOESNT BELONG? Which figure does not belong with the other
three? Explain your reasoning.
6)=3
9+(- 3)=
3+(- 9)=
4+(- =
1)
9+(-
Draw a net of the square pyramid. Then find the surface area of the pyramid.
4.
3.
5.
8
8
3
5
3
5
Find the surface area of the pyramid. The side lengths of the base are equal.
1
6.
5 in.
7.
8.
17 cm
11.4 yd
7 in.
12 cm
6 yd
2
9.
9 ft
10.4 ft
10.
11.
8m
14 in.
3.5 m
6.9 in.
12 ft
4m
8 in.
2.2 in.
12. PAPERWEIGHT A paperweight is shaped like a
triangular pyramid. The base is an equilateral
triangle. Find the surface area of the paperweight.
2 in.
1.7 in.
372
Chapter 8
Surface Area and Volume
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