Tricky Trapezium

Geometry Level pending

In a trapezium \(ABCD\), \(AB\) is parallel to \(CD\) and \(AB\) is less than \(CD\). Angle \(ADC\) is equal to 90 and \(AB\) is equal to \(3r/2\) (where \(r\) is the radius of a circle inscribed in the trapezium). Find the area of the trapezium in terms of \(r\).

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