PQRS IS A TRAPEZIUM WITH PQ||SR. SIDE SR IS PRODUCED TO X SUCH THAT RX=PQ. PROVE THAT AR(PSQ)=AR(QRX)

Answer :

We have a trapezium PQRS , As PQ  | |  SR  , and We extend R as RX  =  PQ  ,  SO 

PQ | | XS , As given PQ  | | SR and we get XS after extend SR to "  X  " .

And we know two parallel line always have same distance between each other ,  So we take that distance =  h  , And our diagram , As :


We know Area of triangle  = $\frac{1}{2}\times Base \times Height$ , So

Area of $∆$ PSQ  = $\frac{1}{2}\times PQ \times h$                           ---------- ( 1 )
And
Area of $∆$ QRX  = $\frac{1}{2}\times RX \times h$      , Given PQ  =  RX  , SO we get

Area of $∆$ QRX  = $\frac{1}{2}\times PQ \times h$                           ---------- ( 2 )

From equation 1 and 2 , we get

Area of $∆$ PSQ  =Area of $∆$ QRX                                                 ( Hence proved )