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.

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