Diagonals of a trapezium ABCD with AB || DC, intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.

Construction: Draw OD perpendicular to DC and OP perpendicular to AB.
In △AOB and △DOC
∠CDO = ∠OBA (Alternate Angles)
∠DCO = ∠OAB (Alternate Angles)
∠DOC = ∠AOB (Vertically opposite angles)
∴By AAA Criterion of Similarity
△AOB ≅ △DOC
∴AB/DC = OP/OD (1)
∴A(△AOB)/A(△DOC) = (AB/DC)² = (2DC/DC)² = 4/1