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

2. 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

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

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

5. Vocabulary
surface area
net

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.

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.

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.

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.

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.

11. 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.

12. 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.

13. 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.

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.

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.

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.

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.

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

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)‏

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.

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)‏

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.

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

24. 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

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

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

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