Let A B C D be a convex quadrilateral with B C=2 and C D=6. Suppose that the centroids of \triangle A B C, \triangle B C D, and \triangle A C D form the vertices of an equilateral triangle. What is the maximum possible value of the area of A B C D ?
Answer Choices
A. 27
B. 16 \sqrt{3}
C. 12+10 \sqrt{3}
D. 9+12 \sqrt{3}
E. 30