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
251 square yards
251 square yards
151 square yards
The formula for the surface area of a square pyramid is given by:
Surface Area = (Base Area) + (0.5 x Perimeter of Base x 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 = 5^2 = 25 square yards
Perimeter of Base = 4 x Base Edge Length = 4 x 5 = 20 yards
Slant Height = √((Base Edge Length/2)^2 + Height^2) = √((5/2)^2 + 25^2) ≈ 25.709 yards
Now, we can substitute these values into the formula:
Surface Area = 25 + (0.5 x 20 x 25.709)
Surface Area ≈ 25 + (0.5 x 20 x 25.709) ≈ 276 square yards
Therefore, the surface area of the square pyramid is approximately 276 square yards, which is the first option.