To find the surface area of a square pyramid, we use the formula:
Surface Area = base area + (1/2)*(perimeter of base)*(slant height)
First, let's find the base area. The base of the square pyramid is a square, so its area is:
Area of base = (side length)^2 = (5 yards)^2 = 25 square yards
Next, let's find the slant height. We can use the Pythagorean theorem, since we have a right triangle formed by the height, slant height, and one of the triangular faces. The height is 25 yards, and the side length of the base is 5 yards, so the slant height can be found as:
Slant height = sqrt( height^2 + (1/2 * side length of base)^2 )
= sqrt( 25^2 + (1/2 * 5)^2 )
= sqrt( 625 + 6.25 )
= sqrt( 631.25 )
≈ 25.1 yards
Now, let's find the perimeter of the base. Since the base is a square, all four sides have the same length:
Perimeter of base = 4 * (side length)
= 4 * 5 yards
= 20 yards
Finally, we can substitute these values into the formula for surface area:
Surface Area = base area + (1/2)*(perimeter of base)*(slant height)
= 25 square yards + (1/2)*(20 yards)*(25.1 yards)
= 25 + 10 * 25.1
≈ 25 + 251
= 276 square yards
Therefore, the surface area of the square pyramid is approximately 276 square yards.