Use the formula for the surface area of a square pyramid to solve for the slight high at the length of the base is 40 and surface area equals 2,800

1 answer

The formula for the surface area of a square pyramid is given by:
Surface Area = base area + (1/2) * perimeter * slant height

We are given that the length of the base (b) is 40 and the surface area (A) is 2800.

Now, we need to solve for the slant height (l).

The base area (b) is equal to l * b / 2, and the perimeter (p) is 4 * b.

Substituting the given values into the formula:
A = (l * b / 2) + (1/2 * p * l)
2800 = (l * 40 / 2) + (1/2 * 4 * 40 * l)
2800 = 20l + 80l
2800 = 100l

To solve for l, divide both sides of the equation by 100:
l = 2800 / 100
l = 28

Therefore, the slant height of the square pyramid is 28.