[tex]\it a)\ \mathcal{A}_{ABD}=\dfrac{\ell^2\sqrt3}{4}=\dfrac{6^2\sqrt3}{4}=\dfrac{36\sqrt3}{4}=9\sqrt3\ cm^2\\ \\ c)\ Ducem\ DM\perp AB \Rightarrow DM-\ \^in\breve a\ell \c{\it t}ime\ \c si\ median\breve a \Rightarrow MB=6:2=3\ cm[/tex]
[tex]\it Compar\ \Delta DMB\ cu\ \Delta DEB\begin{cases}DB\ -\ latur\breve a\ comun\breve a\\ \\ \it \widehat{DBE}=\widehat{DBM}=60^o\\ \\ \it MB=EB=3\ cm\end{cases}\ \stackrel{LUL}{\Longrightarrow}\Delta DMB \equiv \Delta DEB\\ \\ \Rightarrow \widehat{DEB}=\widehat{DMB}=90^o \Rightarrow DE\perp BE\\ \\ b)\ \Delta DMB \equiv \Delta DEB \Rightarrow \mathcal{A}_{DBE}=\mathcal{A}_{DMB}=\dfrac{\mathcal{A}_{DAB}}{2}=\dfrac{9\sqrt3}{2}\ cm^2[/tex]
