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9-8 Surface Area Problem of the Day Which figure has the longer side and by how much: a square with an area of 81 ft 2 or a square with perimeter of 84 ft? a square with a perimeter of 84 ft; by 12 ft
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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