# FINDING THE SURFACE AREA OF A PRISM

When dimensions of a prism are given, we can use the appropriate formula to find surface area of the prism.

The formula given below can be used to find surface area of a prism.

The surface area S of a prism with base perimeter P, height h and base area B is

S  =  Ph + 2B

Example 1 :

Erin is making a jewelry box of wood in the shape of a rectangular prism. The jewelry box will have the dimensions shown below. She plans to spray paint the exterior of the box. How many square inches will she have to paint ?

Solution :

Step 1 :

Identify a base, and find its area and perimeter.

Any pair of opposite faces can be the bases. For example, we can choose the bottom and top of the box as the bases.

Find base area.

B  =  l x w

B  =  12 x 15

B  =  180 square in.

Find perimeter of the base.

P  =  2(12) + 2(15)

P  =  24 + 30

P  =  54 in.

Step 2 :

Identify the height, and find the surface area.

The height h of the prism is 6 inches. Use the formula to find the surface area.

S  =  Ph + 2B

S  =  54(6) + 2(180)

S  =  684 square inches

So, Erin will have to spray paint 684 square inches of wood.

Example 2 :

A brand of uncooked spaghetti comes in a box that is a rectangular prism with a length of 9 inches, a width of 2 inches, and a height of 1 1/2 inches. What is the surface area of the box ?

Solution :

Step 1 :

Identify a base, and find its area and perimeter.

Any pair of opposite faces can be the bases. For example, we can choose the bottom and top of the box as the bases.

Find base area.

B  =  l x w

B  =  9 x 2

B  =  18 square in.

Find perimeter of the base.

P  =  2(9) + 2(2)

P  =  18 + 4

P  =  22 in.

Step 2 :

Identify the height, and find the surface area.

The height h of the prism is 1 1/2 inches. Use the formula to find the surface area.

S  =  Ph + 2B

S  =  22(1 1/2) + 2(18)

S  =  22(3/2) + 36

S  =  33 + 36

S  =  69 square inches

So, the surface area of  the box is 69 square inches.

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