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2016-02-25T22:19:46+05:30
Assuming the parallel sides are AB and CD.

Ar(ΔACD) = Ar(ΔBDC)
(Theorem: Triangles with same base that fall between the same two parallel lines have equal areas)

=> Ar(ΔAOD)+Ar(ΔDOC) = Ar(BOC)+Ar(DOC) (sum of component triangles)
=> Ar(ΔAOD) = Ar(BOC)

Thus proved.
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