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
Rajan@2021Guru
ABCD is a trapezium in which AB| | DC and AB = 2CD. The diagonals AC and BD meet at O. Determine the ratio of areas of triangles AOB and COD.
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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