Question

21) A pyramid has a square base with a side

length of 8 inches, a height of 11 inches and a slant
height, I, of 11.7 inches. Calculate the total surface area of
the pyramid.

Answer 1

Explanation:

the total surface area of such a pyramid is the sum of 5 sides :

1 bottom square (8×8)

4 side triangles (baseline 8, height 11.7)

the inner height of the pyramid we don't need, as the slant height is already given, and that is the height of the triangles of the wall of the pyramid.

the area of a triangle is

baseline × height / 2

if the slant height was unknown, we would have used the inner pyramid height and the side lengths to calculate the slant height.

so, we get a areas

bottom square = 8×8 = 64 in²

a side wall triangle = 8×11.7/2 = 4×11.7 = 46.8 in²

all 4 side triangles = 4×46.8 = 187.2 in²

so, the total surface area is

64 + 187.2 = 251.2 in²