In the given figure we have been asked to find the area of triangle if ABCD is a trapezium in which AB| | DC and AB = 2CD. The diagonals AC and BD meet at O.

ML Aggarwal Avichal Publication class 10, Similarity, chapter 13.3, question no 11

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## Given that.

AB II CD

In Δ AOB and Δ COD

∠OAB = ∠OCD (Alternate interior angles)

∠OBA = ∠ODC (Alternate interior angles)

∠AOB = ∠DOC (Vertically opposite angles)

ΔAOB ~ ΔCOD (AAA similarly)

We know that,

Areabof ΔAOB/Area of ΔCOD (AB/CD)2=(AO/CO)2=(OB/OD)2

(2CD/CD)2 = 4:1