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
251 square yards
251 square yards
276 square yards
276 square yards
151 square yards
151 square yards
To find the surface area of a square pyramid, we use the formula:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
Given that the base edge length is 5 yards and the height is 25 yards:
Base Area = (5 yards)^2 = 25 square yards
Perimeter of Base = 4 * 5 yards = 20 yards
Now, we need to find the slant height. To do this, we can use the Pythagorean theorem:
Slant Height = sqrt((height^2) + (base/2)^2)
= sqrt((25 yards)^2 + (2.5 yards)^2)
= sqrt(625 + 6.25)
= sqrt(631.25)
≈ 25.12 yards
Plugging in the values into the formula:
Surface Area = 25 square yards + (1/2) * 20 yards * 25.12 yards
= 25 square yards + 10 yards * 25.12 yards
= 25 square yards + 251.2 square yards
≈ 276.2 square yards
Rounded to the nearest whole number, the surface area is 276 square yards. Therefore, the correct answer is:
276 square yards