12-2: Surface Area of Prisms and Cylinders

12-2: Surface Area of Prisms and Cylinders•The LATERAL AREA of a solid figure is

the sum of the area of all its lateral faces (the sides of a figure)

•The lateral area of a prism is▫L = Ph, where

P = perimeter of the base h = height

h

12-2: Surface Area of Prisms and Cylinders•The SURFACE AREA of a solid figure is

the sum of the area of all its surfaces (the outside of a figure)

•The surface area of a prism is▫S = Ph + 2B, where

P = perimeter of the base h = height B = area of the base

h

12-2: Surface Area of Prisms and Cylinders•Find the lateral and surface area of the

figure below▫L = Ph S = Ph + 2B

What is Pbase? LATERAL AREA =

What is Abase? Plug into the formula for surface area:

3 cm8 cm

5 cm

2(8) + 2(3) = 22 cm

(8)(3) = 24 cm

S = 110 + 2(24) = 158 cm2

22(5) = 110 cm2

12-2: Surface Area of Prisms and Cylinders•Find the surface area of the figure below

▫L = Ph S = Ph + 2B What is Pbase?

LATERAL AREA =

What is Abase? Plug into the formula for surface area:

We need to find “c” first

4 in3 in

c in13 in

So what is “c”?32 + 42 = c29 + 16 = c2

25 = c2

5 = cWhat is Pbase?12 in

½ (4)(3) = 6 in

S = (12)(13) + 2(6) = 168 in2

(12)(13) = 156 in2

12-2: Surface Area of Prisms and Cylinders•The lateral area of a cylinder

▫L = 2πrh, where r = radius h = height

•The surface area of acylinder is▫S = 2πrh + 2πr2

h h

rr

12-2: Surface Area of Prisms and Cylinders•Find the lateral area and surface area of

the cylinder below▫L = 2πrh S = 2πrh + 2πr2

What is r? What is h?

LATERAL AREA = Plug into the formula for surface area:

11 ft

8 ft8 / 2 = 4 ft

11 ft

S = 2π(4)(11) + 2π(4)2 376.99 ft2

2(4)(11) 276.46 ft2

12-2: Surface Area of Prisms and Cylinders•Find the lateral area and surface area of

the cylinder below▫L = 2πrh S = 2πrh + 2πr2 What is r?

Lateral Area = Surface Area =

6 cm

5 cm188.5 cm2

345.58 cm2

12-2: Surface Area of Prisms and Cylinders•Assignment

▫Worksheet #12-2