AHSME 1962 Problem 18

A regular dodecagon ($12$ sides) is inscribed in a circle with radius $r$ inches. The area of the dodecagon, in square inches, is: $\textbf{(A)}\ 3r^2 \textbf{(B)}\ 2r^2 \textbf{(C)}\ \frac{3r^2\sqrt{3}}{4} \textbf{(D)}\ r^2\sqrt{3} \textbf{(E)}\ 3r^2\sqrt{3}$