In a trapezium ABCD, AB || DC and M is the midpoint of BC. Through M, a line PQ || AD has been drawn which meets AB in P and DC produced in Q, as shown in the adjoining figure. Prove that ar(ABCD) = ar(APQD).

In a trapezium ABCD, AB || DC and M is the midpoint of BC. Through M,

1.	In a trapezium ABCD, AB \|\| DC and M is the midpoint of BC. Through M, a line PQ \|\| AD has been drawn which meets AB in P and DC produced in Q, as shown in the adjoining figure. Prove that ar(ABCD) = ar(APQD).
Answer» In a trapezium ABCD, AB \|\| DC and M is the midpoint of BC. Through M, a line PQ \|\| AD has been drawn which meets AB in P and DC produced in Q, as shown in the adjoining figure. Prove that ar(ABCD) = ar(APQD).