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 251 square yards 251 square yards 1,298 square yards 1,298 square yards 151 square yards 151 square yards 276 square yards
The surface area of a square pyramid formula is:
Surface Area = (base area) + (0.5 x perimeter x slant height)
First, calculate the base area by squaring the base edge length:
Base Area = 5 yards * 5 yards = 25 square yards
Next, calculate the slant height using Pythagorean theorem:
Slant Height = sqrt((base edge/2)^2 + height^2)
Slant Height = sqrt((5/2)^2 + 25^2)
Slant Height = sqrt(6.25 + 625)
Slant Height = sqrt(631.25)
Slant Height ≈ 25.14 yards
Now, calculate the perimeter of the base:
Perimeter = 4 * base edge length = 4 * 5 yards = 20 yards
Finally, plug the values into the formula to find the surface area:
Surface Area = 25 + (0.5 * 20 * 25.14)
Surface Area = 25 + (250.70)
Surface Area ≈ 275.70 square yards
Rounded to the nearest whole number, the surface area of the square pyramid is 276 square yards.
Therefore, the correct answer is:
276 square yards