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)
Responses
151 square yards
151 square yards
276 square yards
276 square yards
1,298 square yards
1,298 square yards
251 square yards
To find the surface area of a square pyramid, we can use the formula:
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 surface area as follows:
Base Area = (base edge length)^2 = 5^2 = 25 square yards
Perimeter of Base = 4 * (base edge length) = 4 * 5 = 20 yards
To find the slant height, we can use the Pythagorean theorem:
Slant Height^2 = (base edge length/2)^2 + height^2
Slant Height^2 = (5/2)^2 + 25^2
Slant Height^2 = 6.25 + 625
Slant Height^2 = 631.25
Slant Height ≈ 25.13 yards
Now we can plug these values into the formula:
Surface Area = 25 + (0.5 * 20 * 25.13)
Surface Area ≈ 25 + (0.5 * 502.6)
Surface Area ≈ 25 + 251.3
Surface Area ≈ 276.3
Rounding to the nearest whole number, the surface area of the square pyramid is 276 square yards.