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

Answer 1

Let's denote the length of one side of the square base as "s" and the height of the pyramid as "h".

The surface area of a square pyramid is calculated using the formula:
Surface Area = Base Area + (1/2 * Perimeter of Base * Slant Height)

Given that the surface area of the square pyramid is 116 inches squared and the total area of the pyramid's four triangular faces is 80 inches squared:
116 = s^2 + (1/2 * 4s * h)
80 = 4 * (1/2 * s * h)

Now we need to solve this system of equations to find the values of "s" and "h".

From the second equation, we can simplify to:
80 = 2s * h
80 = 2sh

Rearranging:
h = 80 / (2s)
h = 40 / s

Now we substitute h=40/s in the first equation:
116 = s^2 + (1/2 * 4s * 40/s)
116 = s^2 + 80

Rearranging and simplifying:
s^2 = 36
s = 6

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