Question

What is the surface area of the right rectangular prism?

Answer 1

Answer:  Choice A) 252 in^2

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Explanation:

Refer to the diagram below.

The red rectangle is 6 inches by 12 inches, so its area is 6*12 = 72 square inches. There are two of these rectangles (one on top, one on the bottom). That accounts for 2*72 = 144 square inches so far.

The purple rectangles are 3 inches by 12 inches, yielding an area of 3*12 = 36 square inches each. That's another 2*36 = 72 square inches when we account for the front and back purple rectangles.

The green rectangles are 6 inches by 3 inches. Each green rectangle is 6*3 = 18 square inches. Having two of them means we'll add on 2*18 = 36 square inches.

Overall, the entire surface area is the sum of all the areas we calculated: 144+72+36 = 252 square inches, which is choice A

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Alternative Method:

• L = 12 = length
• W = 6 = width
• H = 3 = height

SA = surface area of the rectangular prism

SA = 2*(L*W + L*H + W*H)

SA = 2*(12*6 + 12*3 + 6*3)

SA = 2*(72 + 36 + 18)

SA = 2*(126)

SA = 252 in^2

So we get the same answer either way