Area of a quadrilateral

Extend $BE$ to $CD$ at point $G$ . Since point $E$ is the midpoint of $AC$ , area $\triangle BCE =0.5$ and area $\triangle BAE =0.5$ . Since $G$ is the midpoint of $CD$ , area $\triangle BCG=2$ and area $\triangle BGD=2$ .

area $\triangle CEG=2-0.5=1.5$

Since $\triangle CEG \sim \triangle CAD$ , area $\triangle CAD =4\times$ area $\triangle CEG$ , so

area $\triangle CAD=4(1.5)=6$

Finally,

area $ABCD=\triangle ABC + \triangle CAD=1+6=$ $\color{#D61F06}\boxed{\large 7}$