Calculate the area of the yellow region and blue region

The area of the yellow region at the center of the square can be computed as: area of the square minus area of an inscribed circle. We have

$y_1=6^2-\pi(3^2)=36-9\pi$

The area of the yellow region on each equilateral triangle can be computed as: area of an equilateral triangle minus area of two circular sectors then multiply it by $4$ . We have

$y_2=4\left[\dfrac{\sqrt{3}}{4}(6^2)-2\left(\dfrac{60}{360}\right)(\pi)(3^2)\right]=36\sqrt{3}-12\pi$

The blue region is composed of four circular sectors having a central angle of $150^\circ$ each. So the area is

$b=4\left(\dfrac{150}{360}\right)\pi (3^2)=15\pi$

The desired answer is $36-9\pi+36\sqrt{3}-12\pi+15\pi=$ $\boxed{36+36\sqrt{3}-6\pi}$