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MB=1/2MD
=>MB=1/3BD
=>\(S_{BDC}=12\cdot3=36\left(cm^2\right)\)
=>\(S_{ABCD}=72\left(cm^2\right)\)
Ta có: * \(\frac{S_{\Delta ADE}}{S_{\Delta ADB}}=\frac{1}{2}\) mà \(\frac{S_{\Delta ADB}}{S_{ABCD}}=\frac{1}{2}\) suy ra \(\frac{S_{\Delta ADE}}{S_{ABCD}}=\frac{1}{4}\)
* \(\frac{S_{\Delta DCM}}{S_{\Delta DCB}}=\frac{1}{2}\) mà \(\frac{S_{\Delta CDB}}{S_{ABCD}}=\frac{1}{2}\) suy ra \(\frac{S_{\Delta DCM}}{S_{ABCD}}=\frac{1}{4}\)
* \(\frac{S_{\Delta EBM}}{S_{\Delta EBC}}=\frac{1}{2}\) mà \(\frac{S_{\Delta EBC}}{S_{\Delta ABC}}=\frac{1}{2}\) suy ra \(\frac{S_{\Delta EBM}}{S_{\Delta ABC}}=\frac{1}{4}\)
tuy nhiên \(\frac{S_{\Delta EBC}}{S_{ABCD}}=\frac{1}{4}\) suy ra \(\frac{S_{\Delta EBM}}{S_{ABCM}}=\frac{1}{8}\)
Ta lại có: \(\frac{S_{\Delta DEM}}{S_{ABCD}}=S_{ABCD}-\left(S_{\Delta ADE}+S_{\Delta EBM}+S_{\Delta DCM}\right)=1-\left(\frac{1}{4}+\frac{1}{4}+\frac{1}{8}\right)=\frac{3}{8}\)
\(\Rightarrow\) \(S_{ABCD}=S_{\Delta DEM}\div\frac{3}{8}=6\times\frac{8}{3}=16\left(cm^2\right)\)
