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.
a. 251 square yards
b. 151 square yards
c. 1,298 square yards
d. 276 square yards
The formula for the surface area of a square pyramid is given by:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant height)
Given that the base edge length is 5 yards and the height is 25 yards, we can calculate the slant height using the Pythagorean theorem:
slant height = sqrt((base edge / 2)^2 + height^2)
= sqrt((5/2)^2 + 25^2)
= sqrt(6.25 + 625)
= sqrt(631.25)
≈ 25.13
Now, let's calculate the surface area:
Base Area = base edge^2
= 5^2
= 25
Perimeter of Base = 4 * base edge
= 4 * 5
= 20
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant height)
= 25 + (0.5 * 20 * 25.13)
= 25 + (0.5 * 502.6)
= 25 + 251.3
≈ 276.3
Rounding to the nearest whole number, the surface area of the square pyramid is approximately 276 square yards.
Therefore, the correct answer is d. 276 square yards.