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Question
In the following, AC // PS // QR and PQ // DB // SR.
Prove that: Area of quadrilateral PQRS = 2 x Area of the quad. ABCD.
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Solution
In Parallelogram PQRS,
AC // PS // QR and PQ // DB // SR.
Similarly, AQRC and APSC are also parallelograms.
Since ΔABC and parallelogram AQRC are on the same base AC and between the same parallels, then
A( ΔABC ) = `1/2`A(AQRC) ......(i)
Similarly,
A( ΔADC ) = `1/2`A( APSC ) .......(ii)
Adding (i) and (ii), we get
Area of quadrilateral PQRS = 2 x Area of the quad. ABCD.
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