Kẻ \(EH\perp BG\), \(CF\perp BG\)
Ta có: \(S_{ABD}=S_{GBC}=\dfrac{1}{2}.AB.AD=\dfrac{1}{2}.S_{ABCD}\)
\(S_{BAG}=\dfrac{1}{2}.AB.AG=\dfrac{1}{2}.AB.\dfrac{1}{2}AD=\dfrac{1}{4}.AB.AD=\dfrac{1}{2}S_{ABD}\)
\(S_{GEB}=\dfrac{1}{2}.AG.EB=\dfrac{1}{2}.AG.\dfrac{1}{2}.AB=\dfrac{1}{4}.AG.AB=\dfrac{1}{2}S_{ABG}\)
\(\Rightarrow S_{GEB}=\dfrac{1}{2}.\dfrac{1}{2}.\dfrac{1}{2}S_{ABCD}=\dfrac{1}{8}S_{ABCD}=\dfrac{1}{4}S_{GBC}\)
\(\Leftrightarrow\dfrac{1}{2}.EH.BG=\dfrac{1}{4}.\dfrac{1}{2}CF.BG\)
\(\Leftrightarrow EH=\dfrac{1}{4}CF\)
Lại có: \(S_{OBE}=\dfrac{1}{2}OB.EH=\dfrac{1}{2}OB.\dfrac{1}{4}CF=\dfrac{1}{4}S_{OBC}\)
Ta có: \(S_{CBE}=S_{OBE}+S_{OBC}=S_{OBE}+4S_{OBE}=5S_{OBE}\)
\(S_{CBE}=5.10=50\left(cm^2\right)\)
Mà \(S_{CBE}=\dfrac{1}{2}S_{CBA}=\dfrac{1}{4}S_{ABCD}\Rightarrow S_{ABCD}=200\left(cm^2\right)\)
