Question

a right prism has a square base, a surface area of 512 inches squared, and a height of 12 inches. Find the length of the square base

Answer 1

8 inches

Explanation:

Surface area of a prism is:

S = 2A + Ph

where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.

The base is a square, so A = s² and P = 4s:

S = 2s² + 4sh

Given that S = 512 and h = 12:

512 = 2s² + 4s(12)

512 = 2s² + 48s

256 = s² + 24s

0 = s² + 24s - 256

0 = (s + 32) (s - 8)

s = -32, s = 8

Since s must be positive, s = 8 inches.