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
251 square yards
251 square yards
1,298 square yards
1,298 square yards
276 square yards
The formula for the surface area of a square pyramid is:
Surface Area = Base Area + 4 * (1/2 * Base Edge Length * Slant Height)
Given that the base edge length is 5 yards and the height is 25 yards, we can calculate the surface area as follows:
Base Area = (Base Edge Length)^2 = 5 * 5 = 25 square yards
Slant Height can be calculated using the Pythagorean theorem:
Slant Height^2 = (Base Edge Length/2)^2 + Height^2
Slant Height^2 = (5/2)^2 + 25^2
Slant Height^2 = 6.25 + 625
Slant Height^2 = 631.25
Slant Height = sqrt(631.25) ≈ 25.13 yards
Now, we can substitute these values into the formula for the surface area:
Surface Area = 25 + 4 * (1/2 * 5 * 25.13)
Surface Area = 25 + 4 * (125.65)
Surface Area = 25 + 502.6
Surface Area ≈ 528.6 square yards
Rounded to the nearest whole number, the surface area of the square pyramid is 529 square yards.
Therefore, the correct response is:
276 square yards