21. Let $A B C D E F$ be a hexagon such that the diagonals $A D, B E$ and $C F$ intersect at the point $O$, and the area of the triangle formed by any three adjacent points is 2 (for example, area of $\triangle B C D$ is 2 ). Find the area of the hexagon.
21. Ans: 12 .
Since area of $\triangle A B C=$ area of $\triangle F A B, F C / / A B$. Similarly $F C / / E D$.
By the same reason, $F E / / A D / / B C$ and $A F / / B E / / C D$. Thus $O F D E, O D B C$ and $O B A F$ are all parallelogram and each of them has area 4. Thus the total area of the hexagon is 12 .