Question

Look at this rectangular prism:

5 mm
9 mm
1 mm


If all three dimensions are halved, then which of the following statements about its surface area will be true?

Answer 1

Surface area scales with the square of the linear scale factor. Halving each dimension multiplies surface area by (1/2)^2 = 1/4.

Original surface area = 2(5·9 + 5·1 + 9·1) = 2(59) = 118 mm^2.
New surface area = 118 · 1/4 = 29.5 mm^2.

So the surface area is one quarter (a 75% decrease) of the original.