If the surface area of a square pyramid is 65 ft² and the areas of the four triangular faces are 40 ft squared what is the length of one of those sides
Let's denote the side length of the square base of the pyramid as "s" and the height of the pyramid as "h".
The surface area of a square pyramid can be calculated using the formula:
Surface Area = A_base + A_side_1 + A_side_2 + A_side_3 + A_side_4
Surface Area = s^2 + 4(1/2)(s)(h)
Given that the total surface area is 65 ft² and the area of the triangular faces is 40 ft²:
65 = s^2 + 4(1/2)(s)(h)
40 = 4(1/2)(s)(h)
Given that the areas of the triangular faces are all the same:
40 = 4(1/2)(s)(h)
40 = 2sh
So we have the following two equations:
65 = s^2 + 4(1/2)(s)(h)
40 = 2sh
Let's solve for "s" and "h" using these equations.