Question

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

What is the length of one of the sides? Show your work

Answer 1

[AI-generated answer — Bot]

Let's call the side length of the square base s and the triangles' side length t.

Each of the four triangular faces has an area equal to 1/2 * s * t = 80/4 = 20, so t = 40/s.

The surface area of the pyramid is equal to the sum of the areas of the square base and the four triangular faces. Thus, we have:

Surface area = Base area + 4 * Triangle area = s^2 + 4 * 20 = 116
=> s^2 + 80 = 116
=> s^2 = 36
=> s = 6 (taking the positive square root since length cannot be negative)

Therefore, the length of one side is 6.