As shown in the figure below, six semicircles lie in the interior of a regular hexagon with side length 2 so that the diameters of the semicircles coincide with the sides of the hexagon. What is the area of the shaded regioninside the hexagon but outside all of the semicircles?
Answer Choices
A. 6 \sqrt{3}-3 \pi
B. \dfrac{9 \sqrt{3}}{2}-2 \pi
C. \dfrac{3 \sqrt{3}}{2}-\dfrac{\pi}{3}
D. 3 \sqrt{3}-\pi
E. \dfrac{9 \sqrt{3}}{2}-\pi