Use the formula for the surface area of a square pyramid to find the surface area if the base if the base edge length is 5 yards and the height is 25 yards. round to the nearest whole number
151 square yard
1,298 square yards
251 square yards
276 square yards
The formula for the surface area of a square pyramid is given by:
Surface Area = base area + (0.5 * perimeter of base * slant height)
To find the surface area, we need to calculate the base area and the perimeter of the base.
The base area of a square pyramid is equal to the square of the base edge length. In this case, the base edge length is given as 5 yards, so the base area is:
Base Area = (5 yards)^2 = 25 square yards
The perimeter of a square is equal to 4 times the length of one of its sides. In this case, the length of one side of the square base is 5 yards, so the perimeter is:
Perimeter = 4 * 5 yards = 20 yards
Lastly, we need to find the slant height. The slant height can be determined using the Pythagorean Theorem. One leg is the height of the pyramid, which is given as 25 yards, and the other leg is half the base edge length, so:
Slant Height = sqrt((0.5 * base edge length)^2 + height^2)
Slant Height = sqrt((0.5 * 5 yards)^2 + (25 yards)^2)
Slant Height = sqrt((2.5 yards)^2 + (25 yards)^2)
Slant Height = sqrt(6.25 yards^2 + 625 yards^2)
Slant Height = sqrt(631.25 yards^2)
Slant Height ≈ 25.13 yards (rounded to two decimal places)
Now we can plug in the values into the surface area formula:
Surface Area = 25 square yards + (0.5 * 20 yards * 25.13 yards)
Surface Area ≈ 25 square yards + (0.5 * 20 yards * 25.13 yards)
Surface Area ≈ 25 square yards + (10 yards * 25.13 yards)
Surface Area ≈ 25 square yards + 251.3 square yards
Surface Area ≈ 276.3 square yards
Rounded to the nearest whole number, the surface area of the square pyramid is approximately 276 square yards. The closest option is 276 square yards.