The diagram above shows a rectangle \(ABCD\) such that \(E\) is the midpoint of \(BC\) and \(F\) is the midpoint of \(CD\). The diagonal \(BD\) intersects \(AF\) and \(AE\) at \(Q\) and \(T\) respectively. The vertical line \(PS\) passing through \(Q\) is perpendicular to \(AB\) and intersects \(AE\) at \(R\). It is also given that \(AB=CD=12\) and \(BC=AD=6\).

Find the area of the triangle \(\triangle QRT\).

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