1. Preview
Warm Up
California Standards
Lesson Presentation

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. AF3. 1 Use variables in expressions describing geometric quantities (e
AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = pd–the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).
Also covered: AF3.2
California
Standards
1 2

4. Vocabulary
surface area
net

5. 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 an arrangement of two-dimensional figures that can be folded to form a three-dimensional figure.

6. 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

7. Additional Example 1: 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.

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 1: 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.

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. 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.

12. Additional Example 3: Finding the Surface Area of a Cylinder
Find the surface area S of the cylinder. Write your answer in terms of . ft
S = area of curved surface + (2  area of each base)
S = (h  2r) + (2  r2)
Substitute 7 for h and 4 for r.
S = (7  2  4) + (2    42)
S = (7  2  4)+ (2    16)
Simplify the power.

13. Additional Example 3 Continued
Find the surface area S of the cylinder. Write in terms of .
S = 56 + 32
Multiply.
S = ( )p
Use the Distributive Property.
S = 88p
The surface area is about 88p ft2.

14. Check It Out! Example 1
Find the surface area S of each prism.
B. 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.

15. 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.

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

17. S = area of lateral surface + (2  area of each base)
Check It Out! Example 3
Find the surface area S of the cylinder. Write your answer in terms of .
6 ft
9 ft
S = area of lateral surface + (2  area of each base)
S = (h  2r) + (2  r2)
Substitute 9 for h and 6 for r.
S = (9  2  6) + (2    62)
S = (9  2  6) + (2    36)
Simplify the power.

18. Check It Out! Example 3 Continued
Find the surface area S of the cylinder. Write your answer in terms of .
S = 108 + 72
Multiply.
S = ( )p
Use the Distributive Property.
S = 180p
The surface area is about 180p ft2.

19. Lesson Quiz
Find the surface area of each figure. Use 3.14 as an estimate 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.
214 ft2
≈188.4 ft2
208 ft2