Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in. and SA equals 2,800 in^2.
The surface area formula for a square pyramid is given by:
SA = B + 2l
where B is the area of the base and l is the lateral surface area.
The base of the pyramid is a square, so the area of the base is B = s^2, where s is the length of the side of the square.
In this case, the length of the base is given as 40 inches, so the area of the base is B = 40^2 = 1600 in^2.
We are given that the total surface area of the pyramid is SA = 2800 in^2.
Therefore, 2800 in^2 = 1600 in^2 + 2l
Subtracting 1600 in^2 from both sides, we get 1200 in^2 = 2l
Dividing both sides by 2, we find l = 600 in^2.
Therefore, the slant height of the square pyramid is 600 in^2.