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)

Answer 1

The formula for the surface area of a square pyramid is given by:

SA = b + (1/2) * P * l

Where b is the area of the base, P is the perimeter of the base, and l is the slant height.

In this case, the length of the base is given as 40 in and the surface area is given as 2,800 in^2. We need to solve for the slant height.

First, let's find the area of the base:

b = (40 in)^2 = 1600 in^2

Next, let's find the perimeter of the base:

P = 4 * 40 in = 160 in

Now we can substitute these values into the formula to solve for l:

2800 in^2 = 1600 in^2 + (1/2) * 160 in * l

2800 in^2 - 1600 in^2 = (1/2) * 160 in * l

1200 in^2 = 80 in * l

Divide both sides of the equation by 80 in:

(1200 in^2) / (80 in) = l

15 in = l

Therefore, the slant height is 15 in.