Carrom Board

The diagonal of the square is $3.5+6+6+6+3.5=25$ . Let $x$ the side length of the square then by pythagorean theorem, we have

$25^2=x^2+x^2$ $\implies$ $625=2x^2$ $\implies$ $x^2=312.5$

Four quarter circles equal to one circle. So the area of the shaded region is

$A_{shaded}=x^2-\pi (3.5^2)-\pi (3^2)(3)\approx$ $\boxed{189.92}$