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 height 25 yards. Round to the nearest whole number

Answer 1

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

Surface Area = base area + (1/2) * perimeter of base * slant height

First, let's calculate the base area:
The base of the pyramid is a square, and the formula for the area of a square is given by:

Area = length of side * length of side

Base Area = 5 yards * 5 yards = 25 square yards

Next, let's calculate the perimeter of the base:
The perimeter of a square is given by:

Perimeter = 4 * length of side

Perimeter of Base = 4 * 5 yards = 20 yards

Finally, let's calculate the slant height:
The slant height can be found using the Pythagorean theorem along with the height and half the length of the base. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Slant Height = sqrt(height^2 + (0.5 * base length)^2)
Slant Height = sqrt(25 yards^2 + (0.5 * 5 yards)^2)
Slant Height = sqrt(625 yards^2 + 6.25 yards^2)
Slant Height = sqrt(631.25 yards^2) ≈ 25.12 yards

Now, let's use the formula to calculate the surface area:
Surface Area = base area + (1/2) * perimeter of base * slant height
Surface Area = 25 square yards + (1/2) * 20 yards * 25.12 yards ≈ 25 square yards + 250.5 square yards ≈ 275.5 square yards

Therefore, the surface area of the square pyramid, rounded to the nearest whole number, is approximately 276 square yards.