To find the surface area of a square pyramid, we can use the formula:
Surface Area = base area + (0.5 * perimeter of base * slant height)
First, let's calculate the base area:
Base Area = base edge length^2
Base Area = 5^2
Base Area = 25 square yards
Next, let's calculate the perimeter of the base:
Perimeter of Base = 4 * base edge length
Perimeter of Base = 4 * 5
Perimeter of Base = 20 yards
Next, let's calculate the slant height:
Slant Height = square root of ( (0.5 * base edge length)^2 + height^2 )
Slant Height = square root of ( (0.5 * 5)^2 + 25^2 )
Slant Height = square root of ( 2.5^2 + 625 )
Slant Height = square root of ( 6.25 + 625 )
Slant Height = square root of 631.25
Slant Height ≈ 25.12 yards
Now, let's plug these values into the formula for the surface area:
Surface Area = 25 + (0.5 * 20 * 25.12)
Surface Area = 25 + (0.5 * 502.4)
Surface Area = 25 + 251.2
Surface Area ≈ 276.2 square yards
Rounded to the nearest whole number, the surface area of the square pyramid is approximately 276 square yards.