6. If $A B C D$ is a convex quadrilateral, and $E$, $F, G$, $H$ are the centroids of $\triangle A B C, \triangle B C D, \triangle C D A, \triangle D A B$ respectively, then the ratio of the area of quadrilateral $E F G H$ to the area of quadrilateral $A B C D$ is $\qquad$
6. $\frac{1}{9}$.