In Fig, AP || BQ || CR. Prove that ar(AQC) = ar(PBR)

Given: AP || BQ
We can say that perpendicular distance from A to BQ is equal to perpendicular distance from P to BQ. Let it be d1.
ar(AQB) = 1/2 × BQ × d1
ar(PQB) = 1/2 × BQ × d1
∴ ar(AQB) = ar(PQB)
Given: CR || BQ
We can say that perpendicular distance from C to BQ is equal to perpendicular distance from R to BQ. Let it be d2
ar(CQB) = 1/2 × BQ × d2
ar(RQB) = 1/2 × BQ × d2
∴ ar(CQB) = ar(RQB).
ar(AQC) = ar(AQB) + ar(BQC) = ar(PQB) + ar(RQB) = ar(PBR)
∴ ar(AQC) = ar(PBR)