Question

A triangular prism has a length of 8 inches. A larger similar triangular prism has a length of 12 inches.

If 216 square inches of paper is used to wrap the smaller prism with minimum wastage, approximately how many square inches of paper will be required to wrap the larger prism?

486 square inches

243 square inches

324 square inches

540 square inches

Answer 1

324 square inches.

8/12 = 2/3
Therefore 216 is 2/3 of the larger prism.
We want 3/3 so
216/2 = 104
108 + 216 = 324.

Answer 2

Excuse me, 216/2 = 108.

Answer 3

@princesshair -have you confirmed that answer is really 324??

Answer 4

Nothing here is important except the following two things:

1) you have to similar shapes
2) you are dealing with an area (this means square the quantity)

So you square the lengths to get the ratio of the areas:

8²/12² = 216/x
--> "cross multiply"

64x = 216 * 144
--> divide by 64

x = 216 * 144 / 64 = 486,