9-8 Surface Area

Warm UpWarm Up

Lesson PresentationLesson PresentationProblem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

9-8 Surface Area

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

9-8 Surface Area

Problem of the DayWhich 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

9-8 Surface Area

Preview of MA.7.G.2.1 Justify and apply formulas for…surface area of…prisms, pyramids, cylinders…

Sunshine State Standards

9-8 Surface Area

Vocabularysurface areanet

9-8 Surface Area

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

9-8 Surface AreaAdditional Example 1A: Finding the Surface Area

of a PrismFind the surface area S of the prism.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.

9-8 Surface AreaAdditional Example 1A Continued

A: A = 5 2 = 10B: A = 12 5 = 60C: A = 12 2 = 24D: A = 12 5 = 60E: A = 12 2 = 24F: A = 5 2 = 10

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

The surface area is 188 in2.

9-8 Surface AreaAdditional Example 1B: Finding the Surface Area of a

PrismFind the surface area S of each prism.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.

9-8 Surface AreaAdditional Example 1B Continued

Front: 9 7 = 63Top: 9 5 = 45Side: 7 5 = 35

63 2 = 12645 2 = 9035 2 = 70

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

The surface area is 286 cm2.

9-8 Surface AreaCheck It Out: Example 1A

Find the surface area S of the prism.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 EF

9-8 Surface AreaCheck It Out: Example 1A

A: A = 6 3 = 18B: A = 11 6 = 66C: A = 11 3 = 33D: A = 11 6 = 66E: A = 11 3 = 33F: A = 6 3 = 18

S = 18 + 66 + 33 + 66 + 33 + 18 = 234Add 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 EF

9-8 Surface AreaCheck It Out: Example 1B

Find the surface area S of each prism.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 cm8 cm

topfront side

9-8 Surface AreaCheck It Out: Example 1B Continued

Side: 10 8 = 80Top: 10 6 = 60Front: 8 6 = 48

80 2 = 16060 2 = 12048 2 = 96

S = 160 + 120 + 96 = 376 Add the areas of each face.The surface area is 376 cm2.

6 cm 10 cm8 cm

topfront side

9-8 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.

9-8 Surface AreaAdditional Example 2: Finding the Surface Area of a

PyramidFind the surface area S of the pyramid.

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

S = 49 + 4 28S = 49 + 112

Substitute.

S = s2 + 4 ( bh) 12__

S = 72 + 4 ( 7 8)12__

S = 161The surface area is 161 ft2.

9-8 Surface AreaCheck It Out: Example 2

Find the surface area S of the pyramid.

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

S = 25 + 4 25S = 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 ft5 ft