In a trapezium ABCD, it is given that AB║CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that ar(∆AOB) = 84cm2 . Find ar(∆COD).

Answer:

In ∆ AOB and COD

∠???????????? = ∠???????????? (???????????????????????????????? ???????????????????????? ???????? ???????? ∥ ????????)

∠???????????? = ∠???????????? (???????????????????????????????????????? ???????????????????????????????? ????????????????????????)

By AA similarity criterion,

∆AOB ~ ∆COD

If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

area