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)
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.