Colourful Triangle

Given is $\Delta FGH$ . $FH=\sqrt { 18 } \approx 4.24$ , $GH=5$ and $\angle FHG={ 45 }^{ \circ }$ . $B$ and $D$ trisect $FH$ . $AB$ and $ED$ are perpendiculars on $FH$ . $C$ and $E$ trisect $AG$ .

Find: $\frac { ar\Delta HBA+ar\Delta BCD+ar\Delta DEF }{ ar\Delta ABC+ar\Delta CDE+ar\Delta EFG }$ $ar\Delta XYZ$ represents the area of $\Delta XYZ$

Provide your answer upto three decimal places. You can open the image in a new tab for an enlarged one.