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
151 square yards
151 square yards
1,298 square yards
1,298 square yards
251 square yards
251 square yards
276 square yards
We can use the formula for the surface area of a pyramid:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
The base of the pyramid is a square, so the base area is just the length of one side squared:
Base Area = (5 yards)^2 = 25 square yards
To find the slant height, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle with one leg being the height of the pyramid (25 yards) and the other leg being half the length of the base (2.5 yards):
Slant Height = sqrt((25 yards)^2 + (2.5 yards)^2) = sqrt(625 + 6.25) = sqrt(631.25) ≈ 25.12 yards
The perimeter of the base is just 4 times the length of one side:
Perimeter of Base = 4 * 5 yards = 20 yards
Now we can substitute these values into the formula:
Surface Area = 25 square yards + (0.5 * 20 yards * 25.12 yards) ≈ 25 + (0.5 * 20 * 25.12) ≈ 25 + (10 * 25.12) ≈ 25 + 251.2 ≈ 276.2 square yards
Rounding to the nearest whole number, the surface area is approximately 276 square yards.