AMC 12 2011b Problem 16

Rhombus $ABCD$ has side length $2$ and $\angle B = 120^{\circ}$. Region $R$ consists of all points inside of the rhombus that are closer to vertex $B$ than any of the other three vertices. What is the area of $R$?

\textbf{(A)}\ \frac{\sqrt{3}}{3} \textbf{(B)}\ \frac{\sqrt{3}}{2} \textbf{(C)}\ \frac{2\sqrt{3}}{3} \textbf{(D)}\ 1 + \frac{\sqrt{3}}{3} \textbf{(E)}\ 2