ratio between the area of square $wxyz$ and the area of square $ abcd$ equal? 
$ABCD$ is a square  and $H$ is an interior point, which divides  it for four triangles. If  $W$, $X,$ $Y$ and $Z$  are  the centroids of triangles $AHD$, $AHB$, $BHC$ and  $CHD$  respectively ,
    then what is  the ratio between the area of the square  $WXYZ$ and the area of the square  $ABCD$ ? 


Can anyone provide me a hint or a help to go  ? 
Thank you very much 

$XW=YZ=\frac{1}{3}BD$, $XY=WZ=\frac{1}{3}AC$ and $XYZW$ is square. 
Thus, the ratio is $\frac{2}{9}$ because $S_{ABCD}=\frac{1}{2}AC\cdot BD$ and
$$\frac{S_{XYZW}}{S_{ABCD}}=\frac{\frac{1}{3}AC\cdot\frac{1}{3}BD}{\frac{1}{2}AC\cdot BD}=\frac{2}{9}$$
For example, let $M$ is a midpoint of $BH$.
Hence, $$\frac{XY}{AC}=\frac{MY}{MC}=\frac{1}{3}$$
