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 276 square yards 276 square yards 151 square yards 151 square yards 1,298 square yards 1,298 square yards 251 square yards
The formula for the surface area of a square pyramid is given by:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
First, let's find the base area. Since the base is a square, the base area is given by:
Base Area = (side length)^2 = 5^2 = 25 square yards
Next, let's find the perimeter of the base. Since the base is a square, all sides have the same length, which is 5 yards. Therefore, the perimeter of the base is given by:
Perimeter of Base = 4 * side length = 4 * 5 = 20 yards
Lastly, let's find the slant height. The slant height is the height of one of the triangular faces of the pyramid. In this case, the height is given as 25 yards. Therefore, the slant height is 25 yards.
Now we can plug these values into the formula:
Surface Area = 25 + (1/2) * 20 * 25
Surface Area = 25 + 10 * 25
Surface Area = 25 + 250
Surface Area = 275
Rounding to the nearest whole number, the surface area of the square pyramid is 275 square yards.