[tex]\it Din\ \Delta EAB\ avem\ DC||AB\ \stackrel{T.f.a.}{\Longrightarrow}\ \Delta EAB \sim \Delta BDC \Rightarrow \\ \\ \\ \Rightarrow k=\dfrac{AB}{DC}= \dfrac{12}{4}=3\ (raportul \ \ de\ \ asem\breve anare)\\ \\ \\ \dfrac{\mathcal{A}_{EAB}}{\mathcal{A}_{EDC}} =k^2=3^2=9 \Rightarrow \mathcal{A}_{EAB}=9\cdot\mathcal{A}_{EDC} \Rightarrow\mathcal{A}_{EAB}=9(\mathcal{A}_{EAB}-\mathcal{A}_{ABCD})\Rightarrow[/tex]
[tex]\it \Rightarrow \mathcal{A}_{EAB}=9\cdot \mathcal{A}_{EAB}-9\cdot \mathcal{A}_{ABCD} \Rightarrow 9\cdot\mathcal{A}_{ABCD}=8\mathcal{A}_{EAB} \Rightarrow 9\cdot72=8\mathcal{A}_{EAB}\Rightarrow\\ \\ \\ \Rightarrow \mathcal{A}_{EAB}=\dfrac{9\cdot72}{8}=9\cdot9=81\ cm^2[/tex]
