,

Assume that

,

Therefore the area of the rectangular $ABDF$ is $2\times2=4$ square unit. Then we calculate the area of the triangle $EBC$ and $CDF$. After that to get the shaded area, we substract the triangles areas from the rectangular area.

$$\begin{eqnarray*}  \text{Area of }EBC &=& \frac12\times 1\times 1\\ &=&\frac12\\  \text{Area of }CDF &=& \frac12\times1\times2 \\ &=& 1 \end{eqnarray*}$$

,

So the shaded area is

$$4-\frac12 - 1 = \frac52$$

and finally the fraction of the shaded part is

$$\frac{\frac52}{4} = \frac58$$