\(\dfrac{S_{GFH}}{S_{AGE}}=\dfrac{\dfrac{1}{2}GF\cdot GH}{\dfrac{1}{2}AG\cdot GE}=\dfrac{\dfrac{1}{2}\cdot\dfrac{1}{2}AG\cdot\dfrac{1}{2}GE}{\dfrac{1}{2}AG\cdot GE}=\dfrac{1}{4}\\ \Rightarrow S_{GFH}=\dfrac{1}{4}S_{AGE}\left(1\right)\\ \dfrac{S_{AGE}}{S_{ADE}}=\dfrac{GE}{DE}=\dfrac{GH+HE}{DH+HG+HE}=\dfrac{2DH}{3DH}=\dfrac{2}{3}\\ \Rightarrow S_{AGE}=\dfrac{2}{3}S_{ADE}\left(2\right)\\ \dfrac{S_{ADE}}{S_{ADC}}=\dfrac{AE}{AC}=\dfrac{4}{5}\Rightarrow S_{ADE}=\dfrac{4}{5}S_{ADC}\left(3\right)\\ \dfrac{S_{ADC}}{S_{ABC}}=\dfrac{DC}{BC}=\dfrac{5}{6}\Rightarrow S_{ADC}=\dfrac{5}{6}S_{ABC}\left(4\right)\)
\(\left(1\right)\left(2\right)\left(3\right)\left(4\right)\Rightarrow S_{GFH}=\dfrac{1}{4}\cdot\dfrac{2}{3}\cdot\dfrac{4}{5}\cdot\dfrac{5}{6}\cdot S_{ABC}=\dfrac{1}{9}S_{ABC}\)
4 và 5
