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?
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.