Solve the problem. The surface area of a square pyramid is 116 in. and the total area of the pyramid’s four triangular faces is 80 in. What is the length of one of the sides?
The surface area of a pyramid consists of the area of its base plus the areas of its lateral faces. By subtraction, since we know the total surface area and the total area of the lateral faces, the area of the base (which is a square) is $116 - 80 = 36$ square inches. So, the length of one side is $\sqrt{36} = \boxed{6}$ inches.
