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