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.