$\frac{1}{2}=\frac{3}{BC}\to BC=6$$A{{E}^{2}}+A{{D}^{2}}=E{{D}^{2}}\to 1+A{{D}^{2}}=4\to AD=\sqrt{3}$$A{{B}^{2}}+A{{C}^{2}}=D{{C}^{2}}\to {{3}^{2}}+A{{C}^{2}}=36\to AC=3\sqrt{3}$$\left. \begin{align} & {{S}_{ADE}}=\frac{1\times \sqrt{3}}{2}=\frac{\sqrt{3}}{2} \\ & {{S}_{ABC}}=\frac{3\times 3\sqrt{3}}{2}=\frac{9\sqrt{3}}{2} \\ \end{align} \right\}\to {{S}_{EDBC}}=\frac{9\sqrt{3}}{2}-\frac{\sqrt{3}}{2}=4\sqrt{3}$