Squared off II

The regular hexagon is made up of six equilateral triangles wit side lengths of $6$ . Therefore the area of the hexagon is $A_h = 6 \times \frac 12 \times 6 \times 6 \sin 60^\circ = 54\sqrt 3$ . We note that the radius of the circle is $6 \sin 60^\circ = 3 \sqrt 3$ and the area of the circle is $A_O = 27 \pi$ . Therefor the area of the green area is $A_g = A_h-A_O = 54\sqrt 3 - 27 \pi \approx \boxed{8.71}$ .