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

Answer 1

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.