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 in2 .(1 point)

1 answer

The formula for the surface area (SA) of a square pyramid is:

SA = base area + lateral area

The base area of a square pyramid is the area of its base, which in this case is a square. Since the length of the base is 40 in., the area of the base can be calculated as:

base area = 40^2 in^2 = 1600 in^2

Thus, the lateral area can be calculated as:

lateral area = SA - base area = 2800 in^2 - 1600 in^2 = 1200 in^2

The formula for the lateral area of a square pyramid is:

lateral area = (1/2) * perimeter of the base * slant height

Since the base of the pyramid is a square, the perimeter of the base can be calculated as:

perimeter of the base = 4 * length of one side = 4 * 40 in. = 160 in.

Now, we can rearrange the formula for the lateral area to solve for the slant height:

slant height = (2 * lateral area) / perimeter of the base
slant height = (2 * 1200 in^2) / 160 in.
slant height = 15 in.

Therefore, the slant height of the square pyramid is 15 in.