Solve the problem. The surface area of a square pyramid is 116 in.2 and the total area of the pyramid’s four triangular faces is 80 in.2

Question

What is the length of one of the sides? Show your work.(2 points)

Answer 1

Let's start by using the formula for the surface area of a square pyramid:

Surface area = base area + 4 × (area of triangular face)

Since we know the surface area and the area of the triangular faces, we can substitute and solve for the base area:

116 in.2 = base area + 4 × 80 in.2/4
116 in.2 = base area + 80 in.2
Base area = 116 in.2 - 80 in.2
Base area = 36 in.2

Since the base of a square pyramid is a square, we can find the length of one of its sides by taking the square root of its area:

Base area = side2
36 in.2 = side2
Side = √36 in.
Side = 6 in.

Therefore, the length of one of the sides of the square base is 6 inches.