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 and the Surface area equals 2,800^2
The formula for the surface area of a square pyramid is:
Surface Area = base area + (0.5 × perimeter of base × slant height)
Given that the base length is 40 and the surface area is 2800^2, we can solve for the slant height.
Since it is a square pyramid, the base area is given by:
Base Area = length of base^2
= 40^2
= 1600
Plugging the values into the formula, we have:
2800^2 = 1600 + (0.5 × perimeter × slant height)
We know that the perimeter of a square is four times the length of one side. Since the base length is 40, the perimeter of the base is:
Perimeter = 4 × length of base
= 4 × 40
= 160
Now, let's rewrite the formula using the values:
2800^2 = 1600 + (0.5 × 160 × slant height)
Simplifying further:
2800^2 - 1600 = 80 × slant height
2800^2 - 1600 = 80 × slant height
(2800^2 - 1600)/80 = slant height
slant height = (2800^2 - 1600)/80
Using a calculator, we can determine the slant height:
slant height ≈ 78