# Colourful Triangle

Geometry Level 5

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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