MODELING SURFACE AREA OF A PRISM

The surface area of a three-dimensional figure is the sum of the areas of all its surfaces. You know how to use the net of a figure to find its surface area. Now you will discover a formula that you can use.

A. The lateral area L of a prism is the area of all faces except the bases.

L  =  2(160 mm²) + 2(300 mm²)  =  920 mm²

B. The area B of each base is 120 mm².

C. The total area of the bases is sum of the areas of two bases (top and bottom).

That is,

=  120 mm² + 120 mm²  =  240 mm²

D. The surface area S of the prism is the sum of the lateral area L and the total area of the bases,

That is,

=  920 mm² + 240 mm²

=  1160 mm²

Reflect

1. Analyze Relationships Use the net above to answer this question :

How does the product of the perimeter P of the base of the prism and the height h of the prism compare to the lateral area L ?

Ph  =  L

2. Critical Thinking How can you express the surface area S of the prism in terms of P, h, and B? Use your answer to Question 1.

S  =  Ph + 2B

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