Question

In the following, AC // PS // QR and PQ // DB // SR.

Prove that: Area of quadrilateral PQRS = 2 x Area of the quad. ABCD.

Answer 1

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.