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)

251

151

1,298

276

Answer 1

The formula for the surface area of a square pyramid is given by:

Surface area = base area + (0.5 × perimeter of base × slant height)

We are given that the base edge length is 5 yards and the height is 25 yards.

The base area can be found by squaring the base edge length:
Base area = (5 yards)^2 = 25 square yards

The perimeter of the base is equal to 4 times the base edge length:
Perimeter of base = 4 × 5 yards = 20 yards

The slant height can be found using the Pythagorean theorem, where the base edge length is the base and the height is the altitude:
Slant height = √(height^2 + (0.5 × base)^2) = √(25^2 + (0.5 × 5)^2) = √(625 + 6.25) = √631.25 ≈ 25.12 yards

Therefore, the surface area of the square pyramid can be calculated as follows:

Surface area ≈ 25 square yards + (0.5 × 20 yards × 25.12 yards) ≈ 25 + (0.5 × 20 × 25.12) ≈ 25 + (250.6) ≈ 275.6

Rounding to the nearest whole number, the surface area is approximately 276 square yards.

Therefore, the correct answer is 276.