Q19 of 32 Page 6

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.

(CBSE 2005, 09)

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

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(CBSE 2005)

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