10-7 Surface Area

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpIdentify the figure described.

1. two parallel congruent faces, with the other faces being parallelograms

2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles

prism

pyramid

Course 1

10-7 Surface Area

Problem of the Day

Which figure has the longer side and by how much, a square with an area of 81 ft2 or a square with perimeter of 84 ft?

A square with a perimeter of 84 ft; by 12 ft

Course 1

10-7 Surface Area

Learn to find the surface areas of prisms, pyramids, and cylinders.

Course 1

10-7 Surface Area

Vocabulary

surface areanet

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Course 1

10-7 Surface Area

The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net. A net is the pattern made when the surface of a solid figure is layed out flat showing each face of the figure.

Course 1

10-7 Surface Area

Additional Example 1A: Finding the Surface Area of a Prism

Find the surface area S of the prism.

A. Method 1: Use a net.

Draw a net to help you see each face of the prism.

Use the formula A = lw to find the area of each face.

Course 1

10-7 Surface Area

Additional Example 1A Continued

A: A = 5 2 = 10

B: A = 12 5 = 60

C: A = 12 2 = 24

D: A = 12 5 = 60

E: A = 12 2 = 24

F: A = 5 2 = 10

S = 10 + 60 + 24 + 60 + 24 + 10 = 188Add the areas of each face.

The surface area is 188 in2.

Course 1

10-7 Surface Area

Additional Example 1B: Finding the Surface Area of a Prism

Find the surface area S of each prism.

B. Method 2: Use a three-dimensional drawing.

Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

Course 1

10-7 Surface Area

Additional Example 1B Continued

Front: 9 7 = 63

Top: 9 5 = 45

Side: 7 5 = 35

63 2 = 126

45 2 = 90

35 2 = 70

S = 126 + 90 + 70 = 286 Add the areas of each face.

The surface area is 286 cm2.

Course 1

10-7 Surface Area

Try This: Example 1A

Find the surface area S of the prism.

A. Method 1: Use a net.

Draw a net to help you see each face of the prism.

Use the formula A = lw to find the area of each face.

3 in.11 in.

6 in. 11 in.

6 in. 6 in.3 in.

3 in.

3 in.

3 in.

A

B C D E

F

Course 1

10-7 Surface Area

Try This: Example 1A

A: A = 6 3 = 18

B: A = 11 6 = 66

C: A = 11 3 = 33

D: A = 11 6 = 66

E: A = 11 3 = 33

F: A = 6 3 = 18

S = 18 + 66 + 33 + 66 + 33 + 18 = 234

Add the areas of each face.

The surface area is 234 in2.

11 in.

6 in. 6 in.3 in.

3 in.

3 in.

3 in.

A

B C D E

F

Course 1

10-7 Surface Area

Try This: Example 1B

Find the surface area S of each prism.

B. Method 2: Use a three-dimensional drawing.

Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

6 cm 10 cm

8 cm

topfront side

Course 1

10-7 Surface Area

Try This: Example 1B Continued

Front: 10 8 = 80

Top: 10 6 = 60

Side: 8 6 = 48

80 2 = 160

60 2 = 120

48 2 = 96

S = 160 + 120 + 96 = 376 Add the areas of each face.

The surface area is 376 cm2.

6 cm 10 cm

8 cm

topfront side

Course 1

10-7 Surface Area

The surface area of a pyramid equals the sum of the area of the base and the areas of the triangular faces. To find the surface area of a pyramid, think of its net.

Course 1

10-7 Surface Area

Additional Example 2: Finding the Surface Area of a Pyramid

Find the surface area S of the pyramid.S = area of square + 4 (area of

triangular face)

S = 49 + 4 28

S = 49 + 112

Substitute.

S = s2 + 4 ( bh) 12__

S = 72 + 4 ( 7 8)12__

S = 161The surface area is 161 ft2.

Course 1

10-7 Surface Area

Try This: Example 2

Find the surface area S of the pyramid.

S = area of square + 4 (area of triangular face)

S = 25 + 4 25

S = 25 + 100

Substitute.

S = s2 + 4 ( bh) 12__

S = 52 + 4 ( 5 10)12__

S = 125The surface area is 125 ft2.

5 ft

5 ft

10 ft

10 ft

5 ft

Course 1

10-7 Surface Area

The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface.

To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base.

Helpful Hint

Course 1

10-7 Surface Area

Additional Example 3: Finding the Surface Area of a Cylinder

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.

S = area of lateral surface + 2 (area of each base)

Substitute.S = h (2r) + 2 (r2)

S = 7 (2 4) + 2 ( 42)

ft

Course 1

10-7 Surface Area

Additional Example 3 Continued

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.

S 7 8(3.14) + 2 16(3.14)

S 7 25.12 + 2 50.24

The surface area is about 276.32 ft2.

Use 3.14 for .

S 175.84 + 100.48

S 276.32

S = 7 8 + 2 16

Course 1

10-7 Surface Area

Try This: Example 3

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.

S = area of lateral surface + 2 (area of each base)

Substitute.S = h (2r) + 2 (r2)

S = 9 (2 6) + 2 ( 62)

6 ft

9 ft

Course 1

10-7 Surface Area

Try This: Example 3 Continued

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.

S 9 12(3.14) + 2 36(3.14)

S 9 37.68 + 2 113.04

The surface area is about 565.2 ft2.

Use 3.14 for .

S 339.12 + 226.08

S 565.2

S = 9 12 + 2 36

Course 1

10-7 Surface Area

Lesson Quiz

Find the surface area of each figure. Use 3.14 for .

1. rectangular prism with base length 6 ft, width 5

ft, and height 7 ft

2. cylinder with radius 3 ft and height 7 ft

3. Find the surface area of the figure shown.

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Course 1

10-7 Surface Area

214 ft2

188.4 ft2

208 ft2