Surface Area of Pyramids Quick Check 2 of 52 of 5 Items 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) Responses 276 square yards 276 square yards 1,298 square yards 1,298 square yards 151 square yards 151 square yards 251 square yards 251 square yards
To find the surface area of a square pyramid, we use the formula:
Surface area = base area + (1/2) * base edge length * slant height.
Given that the base edge length is 5 yards and the height is 25 yards, we can find the slant height using the Pythagorean theorem.
The slant height is the hypotenuse of a right triangle formed by the base edge length and height.
Using the Pythagorean theorem:
Slant height = sqrt((base edge length/2)^2 + height^2)
= sqrt((5/2)^2 + 25^2)
= sqrt(6.25 + 625)
= sqrt(631.25)
≈ 25.10 yards.
Now, we can calculate the surface area:
Base area = (base edge length)^2
= 5^2
= 25 square yards.
Surface area = base area + (1/2) * base edge length * slant height
= 25 + (1/2) * 5 * 25.10
= 25 + (1/2) * 125.5
= 25 + 62.75
= 87.75 square yards.
Rounding to the nearest whole number, the surface area of the pyramid is 88 square yards.