Problem 6. In quadrilateral $A B C D$, the lengths of sides $B C$ and $C D$ are 2 and 6, respectively. The points of intersection of the medians of triangles $A B C, B C D$, and $A C D$ form an equilateral triangle. What is the maximum value that the area of quadrilateral $A B C D$ can take? If necessary, round your answer to 0.01.

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Problem 6. In quadrilateral $A B C D$, the lengths of sides $B C$ and $C D$ are 2 and 6, respectively. The points of intersection of the medians of triangles $A B C, B C D$, and $A C D$ form an equilateral triangle. What is the maximum value that the area of quadrilateral $A B C D$ can take? If necessary, round your answer to 0.01. Answer: $10 \sqrt{3}+12 \approx 29.32$.

For detailed information about the Olympiad, see the page.