To determine the slant height, you will use what you know about surface area of a pyramid.
The surface area of a square Peerman consists of one square, and four congruent triangles.
We know the length of one side on the square base is 18 inches.
The area of the base then would be 324 in.².
Subtract this from the total surface area.
864-324 = 540 in.²
Divide 540 in.² by 4 because there are four congruent triangles.
540/4= 135 in.²
Each triangle is 135 in.². Now use the formula for area of a triangle to solve for the missing slant height.
A = 1/2 x b x h
135 = 1/2 x 18 x h
135 = 9h
h = 15 inches.
The slant height is 15 inches.