7.2

What Is The Surface Area?

Pg. 6Surface Area of Prisms and Cylinders

7.2 – What Is The Surface Area?Surface Area of Prisms and Cylinders

So far this chapter, you have investigated the names given to three-dimensional solids. Today you will explore different ways to find the surface area of a prism.

7.6 – NETS AND SURFACE AREAAnother way to represent a solid is with a net. When folded, a net will form the three dimensional solid it represents.

 a. With your team, predict what the three-dimensional solid formed by the nets will look like.

cylinder Triangular prism

cubeRectangular prism

b. Find the surface area of the prisms by finding the area of each face and adding them together. Don't forget units.

5

12

5

12

10

12

10

13

5

10

30 30

120 130 50

SA = 360cm2

18 18

90 210

180

150

SA = 666m2

c. Obtain the resource pages from your teacher. Cut out each net and fold along the lines to create the three-dimensional solids. Label the bases and the height of the prisms.

Base

Base

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Base

Base

hei

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t

Base

Base

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t

Base

Base

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t

Base

Base

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d. Amber has a hard time visualizing the shape. She wants to come up with a formula that will work for any prism. Examine the nets you cut out and come up with a formula that will let you find the surface area of any prism.

SA = 2B + PH

7.7 – SURFACE AREAUse the new formula to find the surface area of each shape.

30

22

7

SA = 2B + PHSA = 2(30) + (22)(7)SA = 60 + 154

SA = 214m2

½(6)(8) =

24

9SA = 2B + PHSA = 2(24) + (24)(9)SA = 48 + 216

SA = 264ft2

2410

7.8 – TURNING PRISMSWhat if the bases are not at the top and bottom of the prism?a. Explain how the shape at right is a prism. Is it a rectangular prism? Why or why not?

Two congruent parallel bases

Triangular prism

b. Shade in one of the bases of the prism. Then find the base area.

3 3

303 3

16 3 3

2A

9 3A

c. Find the surface area. Don't forget units.

2SA B PH

2 9 3 18 8SA 218 3 144SA in

7.9 – CYLINDERSWhat if the base is a circle? Find the surface area of the cylinder. a. How do you find the area of one base? Perimeter?

2A r

2C r

b. Change the formula you developed by plugging in the circle formulas. Then find the surface area of the cylinder.

2SA B PH 22 2SA r rH

22 2 2 2 10SA 8 40SA

248SA m