Solve the problem. 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? Show your work
Let x be the length of a side of the square base of the pyramid, and let y be the slant height of the pyramid. The surface area of the pyramid is given by the square base area plus the area of the four triangular faces.
Square base area = x^2
Area of a triangular face = 0.5xy
Total area of the four triangular faces = 4 * 0.5xy = 2xy
The sum of these areas is 116, and the total area of the four triangular faces is 80, so we can write the equation:
x^2 + 2xy = 116
2xy = 80
Now we can solve for x:
x^2 + 2xy = 116
x^2 + 80 = 116
x^2 = 36
x = 6
The length of one side of the pyramid is 6 inches.