Question Number 129077 by Study last updated on 12/Jan/21
Commented by benjo_mathlover last updated on 12/Jan/21
$$\frac{\mathrm{FG}}{\mathrm{8}}\:=\:\frac{\mathrm{5}}{\mathrm{6}}\Rightarrow\mathrm{FG}=\frac{\mathrm{20}}{\mathrm{3}} \\ $$$$\frac{\mathrm{DE}}{\mathrm{8}}=\frac{\mathrm{3}}{\mathrm{6}}\Rightarrow\mathrm{DE}=\mathrm{4} \\ $$$$\mathrm{Area}\:\mathrm{FGED}\:=\:\frac{\mathrm{8}×\mathrm{6}}{\mathrm{2}}−\frac{\frac{\mathrm{20}}{\mathrm{3}}+\mathrm{8}}{\mathrm{2}}×\mathrm{1}−\frac{\mathrm{3}×\mathrm{4}}{\mathrm{2}}\: \\ $$$$\:=\:\mathrm{24}−\left(\frac{\mathrm{10}}{\mathrm{3}}+\mathrm{4}\right)−\mathrm{6} \\ $$$$\:=\:\mathrm{18}−\frac{\mathrm{22}}{\mathrm{3}}\:=\:\frac{\mathrm{32}}{\mathrm{3}} \\ $$