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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