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

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.