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 3�C5 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 6�C8

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 9�C11

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 DOESN��T 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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