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Area within rhombus closest to vertex B

Source: AMC 10 2011 b Problem 20

February 24, 2011
geometryrhombustrigonometryperpendicular bisectorAMC

Problem Statement

Rhombus ABCDABCD has side length 22 and ∠B=120∘\angle B = 120 ^\circ. Region RR consists of all points inside the rhombus that are closer to vertex BB than any of the other three vertices. What is the area of RR?
<spanclass=′latex−bold′>(A)</span> 33<spanclass=′latex−bold′>(B)</span> 32<spanclass=′latex−bold′>(C)</span> 233<spanclass=′latex−bold′>(D)</span> 1+33<spanclass=′latex−bold′>(E)</span> 2 <span class='latex-bold'>(A)</span>\ \frac{\sqrt{3}}{3} \qquad <span class='latex-bold'>(B)</span>\ \frac{\sqrt{3}}{2} \qquad <span class='latex-bold'>(C)</span>\ \frac{2\sqrt{3}}{3} \qquad <span class='latex-bold'>(D)</span>\ 1+\frac{\sqrt{3}}{3} \qquad <span class='latex-bold'>(E)</span>\ 2
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