2011 AMC 10B Problem 20

Rhombus ABCD has side length 2 and \angle B = 120^\circ. Region R consists of all points inside 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} \qquad\textbf{(B)}\ \frac{\sqrt{3}}{2} \qquad\textbf{(C)}\ \frac{2\sqrt{3}}{3} \qquad\textbf{(D)}\ 1 + \frac{\sqrt{3}}{3} \qquad\textbf{(E)}\ 2

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.