Question
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 need to 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:
Base area = (5 yards)^2 = 25 square yards
Perimeter of base = 4 × 5 yards = 20 yards
Now we need to find the slant height. We can use the Pythagorean theorem:
Slant height^2 = (0.5 × base edge length)^2 + height^2
Slant height^2 = (0.5 × 5 yards)^2 + 25 yards^2
Slant height^2 = 0.25 × 25 + 625
Slant height^2 = 6.25 + 625
Slant height^2 = 631.25
Slant height ≈ √631.25 ≈ 25.12 yards
Now, substitute the values into the formula:
Surface area = 25 square yards + (0.5 × 20 yards × 25.12 yards)
Surface area = 25 + (0.5 × 20 × 25.12)
Surface area ≈ 25 + (10 × 25.12)
Surface area ≈ 25 + 251.2
Surface area ≈ 276.2
Therefore, the surface area of the square pyramid is approximately 276 square yards. The closest option is "276 square yards".