\(ABC\) is a triangle in which \(AD\) is the bisector of angle \(A\) such that \(\angle ADB = 120 ^\circ\). \(AB : AC = 3 :1\) and \(AD = 10 \text{ cm}\). \(CE\) is the median on side \(AB\) of triangle \(ABC\). \(O\) is the centroid of the triangle \(ABC\). Through \(O\) a line \(OF \parallel EA\) is drawn. Find the area of triangle \(OFC\) in \(\text{cm}^2 \).

Round your answer to 2 decimal places.

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