Question

Solve the problem. 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? Show your work

Answer 1

Let's use "s" to represent the length of one of the sides of the square base of the pyramid.

We know that the surface area of the pyramid is 116 in.2, so we can write an equation:

s^2 + 4(1/2)*s*l = 116
(Note that the surface area of a pyramid includes the area of its base, which is s^2, and the area of its four triangular faces, which is 4 times the area of one face, which is 1/2 times the base times the height.)

We also know that the total area of the pyramid's four triangular faces is 80 in.2, so we can write another equation:

4(1/2)*s*l = 80

Now we have two equations with two variables (s and l), but we can use the second equation to solve for l in terms of s:

2sl = 80
l = 40/s

We can substitute this expression for l into the first equation:

s^2 + 4(1/2)*s*(40/s) = 116

Simplifying:

s^2 + 80 = 116
s^2 = 36
s = 6

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