Question

ABCD is a trapezium with ABIICD and AB=2CD

Answer 1

given: ABCD is a trapezium with AB||CD.......(1)
and AB = 2 CD......(2)

In the triangles AOB and COD;

∠DOC = ∠ BOA [vertically opposite angles are equal]
∠ CDO = ∠ ABO [alternate interior angles ]
∠ DCO = ∠ BAO 

thus Δ AOB ≈ Δ COD.

by the similarity rule, the ratio of the areas of the similar triangles is the ratio of the square of corresponding sides.
therefore
area(Δ AOB) : area(Δ COD)=AB^2:CD^2
area(Δ AOB) : area(Δ COD)=(2CD)^2:CD^2
area(Δ AOB) : area(Δ COD)=4CD^2:CD^2
area(Δ AOB) : area(Δ COD) = 4 : 1.