AMC 12 2023b Problem 17

Triangle $ABC$ has side lengths in arithmetic progression, and the smallest side has length $6$. If the triangle has an angle of $120^\circ,$ what is the area of $ABC$?

$\textbf{(A) }12\sqrt{3} \textbf{(B) }8\sqrt{6} \textbf{(C) }14\sqrt{2} \textbf{(D) }20\sqrt{2} \textbf{(E) }15\sqrt{3}$