2019 AMC 12B Problem 25

Let ABCD be a convex quadrilateral with BC=2 and CD=6. Suppose that the centroids of \triangle ABC,\triangle BCD, and \triangle ACD form the vertices of an equilateral triangle. What is the maximum possible value of the area of ABCD?

\textbf{(A) } 27 \qquad\textbf{(B) } 16\sqrt3 \qquad\textbf{(C) } 12+10\sqrt3 \qquad\textbf{(D) } 9+12\sqrt3 \qquad\textbf{(E) } 30

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