The closed curve in the figure is made up of 9 congruent circular arcs each of length \dfrac{2 \pi}{3}, where each of the centers of the corresponding circles is among the vertices of a regular hexagon of side 2 . What is the area enclosed by the curve?

**Answer Choices**

A. 2 \pi+6

B. 2 \pi+4 \sqrt{3}

C. 3 \pi+4

D. 2 \pi+3 \sqrt{3}+2

E. \pi+6 \sqrt{3}