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.
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