First, get the area of the square field. The area of the square is side multiplied by side.
A = S x S
A = 12 X 12
A = 144 meters squared
Second, get the area of the circle formed by the sprinkler.
The circle is formed inside the square with a radius of 6 meters (half of the diameter which is 12 meters).
A =

A = 3.1415 x 6^2
A = 113.09733 meters squared.
In order to get the not sprinkled area, subtract the area of the square by the area of the circle.
Not Sprinkled Area = 144 meters squared - 113.09733 meters squared
the final answer is 30.90 meters squared.