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
1,298 square yards
1,298 square yards
276 square yards
276 square yards
251 square yards
251 square yards
151 square yards
The surface area of a square pyramid is given by the formula:
Surface Area = Base Area + 4 * (1/2 * Base Edge Length * Slant Height)
In this case, the base edge length is 5 yards and the height is 25 yards.
First, calculate the base area:
Base Area = (Base Edge Length)^2
Base Area = 5^2
Base Area = 25 square yards
Next, calculate the slant height using the Pythagorean theorem:
Slant Height = √(Height^2 + (1/2 * Base Edge Length)^2)
Slant Height = √(25^2 + (1/2 * 5)^2)
Slant Height = √(625 + 6.25)
Slant Height = √631.25
Slant Height ≈ 25.12 yards
Finally, substitute the values into the surface area formula:
Surface Area = 25 + 4 * (1/2 * 5 * 25.12)
Surface Area = 25 + 4 * (2.5 * 25.12)
Surface Area = 25 + 4 * 62.8
Surface Area = 25 + 251.2
Surface Area ≈ 276.2
Rounding to the nearest whole number, the surface area of the square pyramid is 276 square yards.