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matlab
In △ADC, by mid point
theorem, SR∥AC,SR=21(AC)
Similarly PQ∥AC,PQ=21(AC)
⇒PQ∥RS, similarly PS∥QR
⇒ opposite sides parallel
⇒PQRS is a parallelogram
As △ALS∼△AOD (AA similarity)
⇒ODSL=ADAS=21
⇒ Area of rectangle SL×R
=SL×L×=21(OD)(2AC)
{LX×=SR=2AC}=21(ar△ACD)
⇒ Area of PQRS=21(arACD)
+21(arACB)=21(arABCD)

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