1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Identify the figure described.
Warm Up
Identify 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 2

3. 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 3

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

5. Vocabulary
surface area
net 5

6. 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. 6

7. Additional Example 1A: Finding the Surface Area of a Prism
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. 7

8. 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
Add the areas of each face.
S = = 188
The surface area is 188 in2. 8

9. Additional Example 1B: Finding the Surface Area of a Prism
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. 9

10. Additional Example 1B Continued
Front: 9  7 = 63
63  2 = 126
Top: 9  5 = 45
45  2 = 90
Side: 7  5 = 35
35  2 = 70
S = = 286
Add the areas of each face.
The surface area is 286 cm2. 10

11. Find the surface area S of the prism. Method 1: Use a net.
Check It Out: Example 1A
Find the surface area S of the prism.
Method 1: Use a net. A
3 in.
3 in.
6 in.
6 in.
3 in.
3 in.
6 in.
11 in.
11 in. B C D E F
3 in.
Draw a net to help you see each face of the prism.
Use the formula A = lw to find the area of each face. 11

12. Add the areas of each face. S = 18 + 66 + 33 + 66 + 33 + 18 = 234
Check It Out: Example 1A
A: A = 6  3 = 18 A
3 in.
B: A = 11  6 = 66
3 in.
6 in.
6 in.
3 in.
C: A = 11  3 = 33
11 in.
D: A = 11  6 = 66 B C D E
E: A = 11  3 = 33 F
3 in.
F: A = 6  3 = 18
Add the areas of each face.
S = = 234
The surface area is 234 in2. 12

13. Find the surface area S of each prism.
Check It Out: Example 1B
Find the surface area S of each prism.
Method 2: Use a three-dimensional drawing.
top
side
front
8 cm
10 cm
6 cm
Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces. 13

14. Check It Out: Example 1B Continued
top
side
front
8 cm
10 cm
6 cm
Front:  6 = 48
48  2 = 96
Top:  6 = 60
60  2 = 120
Side:  8 = 80
80  2 = 160
S = = 376
Add the areas of each face.
The surface area is 376 cm2. 14

15. 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. 15

16. 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 = s2 + 4  ( bh) 1 2 __
S =  (  7  8) 1 2 __
Substitute.
S =  28
S =
S = 161
The surface area is 161 ft2. 16

17. Find the surface area S of the pyramid.
Check It Out: Example 2
Find the surface area S of the pyramid.
S = area of square + 4  (area of triangular face)
10 ft
5 ft
S = s2 + 4  ( bh) 1 2 __
5 ft
S =  (  5  10) 1 2 __
Substitute.
10 ft
S =  25
5 ft
S =
S = 125
The surface area is 125 ft2. 17

18. 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 18

19. Additional Example 3: Finding the Surface Area of a Cylinder
Find the surface area S of the cylinder. Use for , and round to the nearest hundredth. ft
S = area of curved surface + 2  (area of each base)
S = h  (2r) + 2  (r2)
Substitute.
S = 7  (2    4) + 2  (  42) 19

20. Additional Example 3 Continued
Find the surface area S of the cylinder. Use for , and round to the nearest hundredth.
S = 7  8 + 2  16
S  7  8(3.14) + 2  16(3.14)
Use 3.14 for .
S  7   50.24
S 
S 
The surface area is about ft2. 20

21. S = area of curved surface + 2  (area of each base)
Check It Out: Example 3
Find the surface area S of the cylinder. Use for , and round to the nearest hundredth.
6 ft
9 ft
S = area of curved surface + 2  (area of each base)
S = h  (2r) + 2  (r2)
Substitute.
S = 9  (2    6) + 2  (  62) 21

22. Check It Out: Example 3 Continued
Find the surface area S of the cylinder. Use for , and round to the nearest hundredth.
S = 9  12 + 2  36
S  9  12(3.14) + 2  36(3.14)
Use 3.14 for .
S  9  
S 
S  565.2
The surface area is about ft2. 22

23. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 23

24. Find the surface area of each figure. Use 3.14 for .
Lesson Quiz
Find the surface area of each figure. Use for .
1. rectangular prism with base length 6 ft, width ft, and height 7 ft
2. cylinder with radius 3 ft and height 7 ft
3. Find the surface area of the figure shown.
214 ft2
188.4 ft2
208 ft2 24

25. Lesson Quiz for Student Response Systems
1. Find the surface area of a rectangular prism with base length 7 ft, width 6 feet, and height 9 ft.
A. 318 ft2
B. 306 ft2
C. 300 ft2
D. 298 ft2 25

26. Lesson Quiz for Student Response Systems
2. Find the surface area of a cylinder with radius 5 ft and height 8 ft. Use 3.14 for 
A ft2
B ft2
C ft2
D ft2 26

27. Lesson Quiz for Student Response Systems
3. Find the surface area of the figure shown.
A. 162 ft2
B. 152 ft2
C. 142 ft2
D. 132 ft2 27