A problem by Efren Medallo

Geometry Level 1

In the figure above, $$\Delta ABC \cong \Delta DEF$$ 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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