2023 AMC 12B 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} \qquad \textbf{(B)} 8\sqrt{6} \qquad \textbf{(C)} 14\sqrt{2} \qquad \textbf{(D)} 20\sqrt{2} \qquad \textbf{(E)} 15\sqrt{3}

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