A problem by Efren Medallo

Geometry Level 2

In the figure, $\Delta ABC \cong \Delta EDF$ with $\overline{AC} = \overline{EF} = 8$ .

If $\Delta DEF$ is positioned in such a way that $D$ lies along $\overline{AB}$ and the area of polygon $ADEC$ is $28,$ what is the length of $\overline{FC}?$

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