Triangle Trigonometry and Vectors · Superchallenge problem

In $\triangle ABC$, $\overrightarrow{AB}\cdot\overrightarrow{AC}=6$, $\overrightarrow{BA}\cdot\overrightarrow{BC}=10$, and $\overrightarrow{CA}\cdot\overrightarrow{CB}=15$. Find the area of the triangle.