2013 AMC 10B Problem 7

Six points are equally spaced around a circle of radius 1. Three of these points are the vertices of a triangle that is neither equilateral nor isosceles. What is the area of this triangle?

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

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