Question in description

Question

1. If the dimensions of a square prism are increased to three times their original length, by what factor would the lateral surface area be affected?

Answer 1

Let x be the dimensions of the square base and y be the height of the square prism. The surface area of a square prism:

SA = 2•Base_Area + Lateral_Area = 2x²+4xy

We are interested in the lateral surface area or 4xy.

if x₂=3x and y₂ = 3y then

LA₂ = 4(3x)(3y) = 4 • 9xy

Factor = LA₂/LA = 4•9xy/4xy = 9