The total surface area of a pyramid with a square base is 384 ft squared. It's base edges are 12 ft long. Find the height of the pyramid

Surface area = area of base + 4 * area of each triangular face

The slant height of each face = sqrt (6^2 + h^2) where h = height.

so we can create an equation:-

12^2 + 4 * 1/2 * 12 * sqrt (6^2 + h^2) = 384

The height of the pyramid is 8

sqrt (36+h^2) = (384 - 144) / 24 = 240/24 = 10

36+h^2 = 100

h^2 = 64

h = 8 ft