A circle with centre \(O\) is circumscribed about the \(\triangle ABC \) with \(\angle A\) as an obtuse angle. The radius \(AO\) forms an angle \(30\) with the altitude \(AH\) on \(BC\). The extension of angle bisector of \(\angle A\) meets \(BC\) at \(F\) and the circumference of the circle at \(L\) and the radius \(AO\) intersects \(BC\) at point \(E\). Compute the area of the quadrilateral \(FEOL\) if it is known that \(AL=4\sqrt{2}\) \(\text{cm}\) and \(AH=\sqrt{2\sqrt{3}}\) \(\text{ cm}\).

If your answer comes as \(a(b-\sqrt{c})\) \(\text{ cm}^{2}\) submit it as \(a+b+c\).

**Note :** All angles are in degree.

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