Answer
$36\pi-72\approx41.1\ unit^2$
Work Step by Step
Step 1. Based on the given conditions, we have the radius of the circle $r=6$
Step 2. The diagonal of the square is the diameter of the circle $D=2r=12$
Step 3. The side length of the square is $s=\frac{D}{\sqrt 2}=6\sqrt 2$
Step 4. The area of the square is $A=s^2=72\ unit^2$
Step 5. Area of the blue region is $B=\pi r^2-A=36\pi-72\approx41.1\ unit^2$
