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Construct a quadrilateral \(PQRS\) with \(PQ = QR = 5 \ cm\), \(\angle QPR = 50^{\circ}\), \(\angle PRS = 40^{\circ}\) and \(\angle RPS= 80^{\circ}\). Also, find its area.
 
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This is a self-assessment task. Solve this question and assess the solution steps after completing the test on your own.