Question

The surface area of a square Pyramid is 116in and the total area of the Pyramid's four triangular faces is 80 in. What is the length of one of the sides?

Answer 1

Let s be the length of one of the sides of the square base, and h be the height of the pyramid. We know that the surface area of the pyramid is:

SA = s^2 + 4s(h/2)

Simplifying this equation, we get:

116 = s^2 + 2sh

We also know that the total area of the four triangular faces is:

80 = 4(1/2)sh

Simplifying this equation, we get:

40 = sh

Now we can substitute sh into the first equation:

116 = s^2 + 2(40)

116 = s^2 + 80

Subtracting 80 from both sides, we get:

36 = s^2

Taking the square root of both sides, we get:

s = 6

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