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

Answer 1

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