Use the formula for surface area of a square pyramid to solve for the slant height if the length of the base is 40 in and the cell and the surface area equals 2800 inches squared
The formula for the surface area of a square pyramid is:
Surface area = base area + lateral area
The base area of a square pyramid is given by the formula:
Base area = length of base x width of base
Since this is a square pyramid, the length of the base is equal to the width of the base. Let's denote the length of the base as "B".
Now, let's consider the lateral area of the square pyramid. The lateral area is given by the formula:
Lateral area = perimeter of base x slant height / 2
Since this is a square pyramid, the perimeter of the base is given by:
Perimeter of base = 4 x length of base = 4B
Given that the surface area of the square pyramid is 2800 inches squared, we can set up the equation:
2800 = B^2 + (4B x slant height) / 2
Simplifying this equation gives:
2800 = B^2 + 2B x slant height
Since we are given that the length of the base is 40 inches, we can substitute B = 40 into the equation:
2800 = 40^2 + 2(40) x slant height
2800 = 1600 + 80 x slant height
2800 - 1600 = 80 x slant height
1200 = 80 x slant height
Dividing both sides of the equation by 80 gives:
15 = slant height
Therefore, the slant height of the square pyramid is 15 inches.