In △APS and △QRB
⇒ ∠PAS=∠QBR=90o [ Given ]
⇒ ∠PSA=∠RQB [ Alternate angles ]
⇒ PS=QR [ Opposite sides of rectangle are equal ]
∴ △APS≅△QRB [ By AAS congruence rule ]
⇒ Ar(△APS)=Ar(△QRB) [ Area of two congruent triangles are equal ]
⇒ PA=RB [ By C.P.C.T. ]
In △PQS and △QRS
⇒ PS=QR [ Opposite sides of rectangle are equal ]
⇒ QS=QS [ Common sides ]
⇒ PQ=RS [ Opposite sides of rectangle are equal ]
∴ △PQS≅△QRS [ By SSS rule ]
The area of two congruent triangles are equal.
∴ Ar(△PQS)=Ar(△QRS)