Use the formula for the surface area of a square pyramid to find the surface area if the base edge length is 5 yards and the height is 25 yards. Round to the nearest whole number.
(1 point)
The surface area of a square pyramid is calculated by the formula:
Surface area = (base area) + 1/2 * (perimeter of base) * slant height
First, calculate the base area:
Base area = side length^2
Base area = 5 yards * 5 yards
Base area = 25 square yards
Next, calculate the slant height:
Using the Pythagorean theorem:
slant height = sqrt((1/2 * base edge length)^2 + height^2)
slant height = sqrt((1/2 * 5)^2 + 25^2)
slant height = sqrt(6.25 + 625)
slant height = sqrt(631.25)
slant height ≈ 25.12 yards
Now, calculate the surface area:
Surface area = 25 + 1/2 * (4 * 5) * 25.12
Surface area = 25 + 1/2 * 20 * 25.12
Surface area = 25 + 250.6
Surface area ≈ 275.6 square yards
Rounded to the nearest whole number:
Surface area ≈ 276 square yards