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

151 square yards
151 square yards

276 square yards
276 square yards

251 square yards
251 square yards

1,298 square yards

Answer 1

The formula for the surface area of a square pyramid is SA = base area + (1/2) * perimeter * slant height.

First, let's calculate the base area:

Base area = length of the base edge^2
Base area = 5^2 = 25 square yards

Next, let's calculate the perimeter:

Perimeter = 4 * length of the base edge
Perimeter = 4 * 5 = 20 yards

Now, let's find the slant height. We can use Pythagorean theorem to find it:

(1/2) * base edge^2 + height^2 = slant height^2
(1/2) * 5^2 + 25^2 = slant height^2
(1/2) * 25 + 625 = slant height^2
12.5 + 625 = slant height^2
637.5 = slant height^2
slant height ≈ √637.5
slant height ≈ 25.25 yards

Now, let's substitute these values into the formula for surface area:

SA = 25 + (1/2) * 20 * 25.25
SA = 25 + 10 * 25.25
SA = 25 + 252.5
SA ≈ 277.5 square yards

Rounded to the nearest whole number, the surface area of the square pyramid is 278 square yards.