In a trapezium ABCD, O is the point of intersection of AC and BD, AB|| CD and AB = 2 x CD. If area of ΔAOB = 84 cm², find the area of ΔCOD.

Question

In a trapezium ABCD, O is the point of intersection of AC and BD, AB|| CD and AB = 2 x CD. If area of ΔAOB = 84 cm 2 , find the area of ΔCOD.

Philoid · Accepted Answer

Given :

AB|| CD

AB = 2 x CD

⇒

∠AOB = ∠COD (Vertically Opposite angles)

∠DCO = ∠OAB (Alternate Angles)

So ΔAOB & ΔDOC are similar by the A.A. (Angle Angle) axiom of Similarity

Since both the triangles are similar so according to the Area –Length relations of similar triangle we can write

⇒

Area of ∆DOC = 21cm²