2000 PMWC Problems/Problem T6

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In $\triangle ABC$, $BC=6BD$, $AC=5EC$, $DG=GH=HE$, $AF=FG$. Find the ratio of the area of $\triangle FGH$ to the area of $\triangle ABC$.

[asy] fill((1,2.5)--(0.9,0.72)--(1.82,1.46)--cycle,black); draw((0,5)--(-3,0)--(4,0)--(0,5)--(0,0)); draw((0,0)--(2.5,2)); draw((0,5)--(1,2.5)--(0.9,0.72)); draw((1,2.5)--(1.82,1.46)); label("$A$",(0,5),N); label("$B$",(-3,0),W); label("$C$",(4,0),E); label("$D$",(0,0),S); label("$E$",(2.5,2),NE); label("$F$",(1,2.5),E); label("$G$",(0.9,0.72),S); label("$H$",(1.82,1.46),S); //Credit to chezbgone2 for the diagram[/asy]


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