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 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.