Area after folding

Geometry Level 4

In the figure, \(ABCD\) is a parallelogram with the height of \(x\) cm. It is known that \(AB\) is 6 cm longer than the height and \(AD\) is 3 cm longer than 4 times of the height.

\(AB\) and \(CD\) are then folded along \(AP\) and \(QC\) respectively to form \(AB'\) and \(CD'\) respectively. Similarly, \(BP\) and \(QD\) are folded along \(AP\) and \(QC\) respectively to form \(PB'\) and \(QD'\).

It is known that \(AB'CD'\) is a rhombus, find the area of \(AB'CD'\).

Note: The figures are not drawn to scale.

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