Question

Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40in and SA equals 2800 inches squared

Answer 1

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

SA = B + (1/2)Pl

Where:
SA is the surface area
B is the area of the base
P is the perimeter of the base
l is the slant height

In this case, we are given that the length of the base is 40in and the surface area is 2800in². We can proceed to solve for the slant height.

First, we need to find the area of the base (B) and the perimeter of the base (P). Since the base is a square, all sides are equal in length.

The area of a square is found by squaring the length of one side, so:
B = 40^2 = 1600in²

The perimeter of a square is found by multiplying the length of one side by 4, so:
P = 4 * 40 = 160in

Now we can substitute these values into the formula:

2800 = 1600 + (1/2)(160)(l)

Multiplying the terms:
2800 = 1600 + 80l

Rearranging the equation:
80l = 2800 - 1600
80l = 1200

Finally, we solve for l:
l = 1200 / 80
l = 15

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