\[\boxed{\mathbf{243}\mathbf{.}}\]
\[S_{\text{AOE}} = 6\ см^{2}.\]
\[1)\ S_{\text{AOD}} = 6 \cdot 2 = 12\ см^{2}.\]
\[2)\ S_{\text{BAD}} = 12 \cdot 2 = 24\ см^{2}.\]
\[3)\ S_{\text{ABCD}} = 24 \cdot 2 = 48\ см^{2}.\]