Question

The diagonal of a trapezium ABCD in which AB|| DC , intersect at O.If AB = 2CD then find the ratio of area of triangels AOB and COD.

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Answer 1

by the Thales theoram or property of similarity
given =AB = 2CD
AB /CD = 2/1
In tri.AOB and COD
area of triangle AOB / AREA OF tri. COD
BY APPLYING SIDES = 2/1
AB2 / CD2
AB = 2
CD =1
RATIO IS AB2 / CD2
4:1

Answer 2

Hey See the attached pic

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Given :-

ABCD is a Trapezium , AB parallel DC , Diagonal intersect at O and AB = 2 DC

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Find :-

ΔAOB ÷ ΔCOD

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Proof :-

In ΔAOB and ΔCOD

∠DOC = ∠BOA (V•O•A)

∠CDO =  ∠ABO (A•I•A)

So :-

Δ AOB ≈ Δ COD (Similarity Rule)

Now :-

ar(ΔAOB) ÷ (ΔCOD) = AB² ÷ CD²

(2CD)² ÷ (CD)²

(4CD)² ÷ (CD)²

= 4

ar(ΔAOB) : ar(ΔCOD)

= 4 : 1

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