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 region-inside 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