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)
• 151 square yards
• 251 square yards
1,298 square yards
• 276 square yards
To find the surface area of a square pyramid, you use the formula:
Surface Area = base area + (1/2 * base perimeter * slant height)
First, calculate the base area:
Base edge length = 5 yards
Base area = 5 * 5 = 25 square yards
Next, calculate the slant height:
Height = 25 yards
Slant height = sqrt((5/2)^2 + 25^2) = sqrt(6.25 + 625) = sqrt(631.25) ≈ 25.13 yards
Now plug the values into the formula:
Surface Area = 25 + (1/2 * 20 * 25.13) ≈ 25 + (10 * 25.13) ≈ 25 + 251.3 ≈ 276.3 square yards
Rounding to the nearest whole number, the surface area is approximately 276 square yards.
So, the correct answer is:
• 276 square yards.