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) Responses 1,298 square yards 1,298 square yards 276 square yards 276 square yards 251 square yards 251 square yards 151 square yards 151 square yards
The formula for the surface area of a square pyramid is given as:
Surface Area = base area + (0.5 * perimeter of base * slant height)
First, we need to find the perimeter of the base. Since a square has all sides equal in length, the perimeter of the base would be 4 times the length of one side.
Perimeter of base = 4 * 5 yards = 20 yards
Next, we need to find the slant height. The slant height can be found using the Pythagorean theorem, where the height is one leg, the length of half the base is the other leg, and the slant height is the hypotenuse.
Using the Pythagorean theorem:
slant height^2 = height^2 + ((1/2 * base edge length)^2)
= 25^2 + (0.5 * 5)^2
= 625 + 1.25
= 626.25
Taking the square root of both sides:
slant height ≈ 25
Now, we can plug in the values into the surface area formula:
Surface Area = base area + (0.5 * perimeter of base * slant height)
= 5^2 + (0.5 * 20 * 25)
= 25 + (0.5 * 500)
= 25 + 250
= 275
Rounding to the nearest whole number:
Surface Area ≈ 275 square yards
Therefore, the surface area of the square pyramid is approximately 275 square yards.