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
The formula for the surface area of a square pyramid is
SA = B + (1/2) * Pl
where B is the area of the base, P is the perimeter of the base, and l is the slant height.
Given that the length of the base is 40 inches, we can calculate B and P. Since the base is a square, the area of the base is B = 40 * 40 = 1600 square inches.
Since each side of the square base has a length of 40 inches, the perimeter of the base is P = 4 * 40 = 160 inches.
We are also given that the surface area of the pyramid is SA = 2800 square inches. Therefore, we can substitute these values into the formula and solve for l:
2800 = 1600 + (1/2) * 160 * l
Subtracting 1600 from both sides, we get:
1200 = 80 * l
Dividing both sides by 80, we find:
l = 1200 / 80 = 15 inches.
Therefore, the slant height of the square pyramid is 15 inches.