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)

Question

Responses

1,298 square yards
1,298 square yards

276 square yards
276 square yards

151 square yards
151 square yards

251 square yards

Answer 1

To find the surface area of a square pyramid, we use the formula:

Surface Area = base area + (4 * (1/2 * base edge length * slant height))

Given that the base edge length is 5 yards and the height is 25 yards:

Base Area = (base edge length)^2
Base Area = 5^2
Base Area = 25 square yards

To find the slant height, we can use 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 ≈ 25.14 yards

Now, we can substitute these values into the formula:

Surface Area = 25 + (4 * (1/2 * 5 * 25.14))
Surface Area = 25 + (4 * (2.5 * 25.14))
Surface Area = 25 + (4 * 62.85)
Surface Area = 25 + 251.4
Surface Area ≈ 276 square yards

Therefore, the surface area of the square pyramid is approximately 276 square yards.