The pyramid shown has a square base that is 18 inches on each side. It has a surface area of 864 square inches. What is the slant height

The first step is to find the relationship between the square base and the surface area.

Surface area (SA) = area of the square (SS) + area of triangles. 4 (AT)

Thus we can conclude area of triangles 4 (AT) = SA - SS = 864 - (18*18)

4 (AT) = 864 - 324 = 540

Each triangle = 540/4 = 135 square in.

An area of one triangle (AT) = (base * slant height) / 2

The base = 18 in.

slant height = 2 (AT) / base = 2 (135) / 18 = 15