Ta thấy: [tex]\frac{S_{AOB}}{S_{AOD}}=\frac{S_{BOC}}{S_{COD}}=\frac{BO}{OD}\Rightarrow \left\{\begin{matrix} S_{AOB}=\frac{BO}{OD}*S_{AOD}\\ S_{BOC}=\frac{BO}{OD}*S_{COD} \end{matrix}\right.\Rightarrow S_{ABC}=\frac{BO}{OD}*S_{ADC}[/tex]
Lại có:[tex]\frac{S_{ABC}}{S_{ACD}}=\frac{AB}{CD}=\frac{1}{3}\Rightarrow S_{ABC}=\frac{1}{3}*S_{ACD}\Rightarrow \frac{BO}{OD}=\frac{1}{3}\Rightarrow \frac{OD}{BO}=3\Rightarrow S_{AOD}=\frac{DO}{BO}*S_{AOB}=3*5=15(cm^2)\Rightarrow S_{ABD}=15+3=18(cm^2)[/tex]
Lại có: [tex]S_{ABD}=S_{ABC}\Rightarrow S_{ABC}=18(cm^2)\Rightarrow S_{ACD}=3*S_{ABC}=54(cm^2)\Rightarrow S_{ABCD}=18+54=72(cm^2)[/tex]