Let's start by using the formula for the surface area of a square pyramid:
SA = s^2 + 2s(l)
Where SA is the surface area, s is the length of one of the sides of the square base, and l is the slant height of the pyramid.
We are given that the surface area is 116 in.2, so we can write:
116 = s^2 + 2s(l)
We are also given that the total area of the four triangular faces is 80 in.2. Since each face is a triangle with base s and height l, we can write:
80 = 4(0.5s)(l)
80 = 2sl
Now we have two equations with two variables (s and l). We can use the second equation to solve for l in terms of s:
l = 40/s
Substitute this expression for l into the first equation:
116 = s^2 + 2s(l)
116 = s^2 + 2s(40/s)
116 = s^2 + 80
Simplify:
s^2 = 36
Take the square root of both sides:
s = 6
Therefore, the length of one of the sides is 6 inches.
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
What is the length of one of the sides?
1 answer