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2011 AMC 10B Question 20

AMC10 · 2011 AMC 10B

Question 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 $R?$
  1. $\dfrac{\sqrt{3}}{3} $
  2. $\dfrac{\sqrt{3}}{2} $
  3. $\dfrac{2\sqrt{3}}{3} $
  4. $1 + \dfrac{\sqrt{3}}{3} $
  5. $2 $