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Home » In a trapezium ABCD, it is given that AB║CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that ar(∆AOB) = 84cm2 . Find ar(∆COD).
In a trapezium ABCD, it is given that AB║CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that ar(∆AOB) = 84cm2 . Find ar(∆COD).
CBSE | Class 10 | Exercise 4E | Maths | RS Aggarwal | Triangles
In a trapezium ABCD, it is given that AB║CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that ar(∆AOB) = 84cm2 . Find ar(∆COD).

 

 

Answer:

In ∆ AOB and COD

∠???????????? = ∠???????????? (???????????????????????????????? ???????????????????????? ???????? ???????? ∥ ????????)

∠???????????? = ∠???????????? (???????????????????????????????????????? ???????????????????????????????? ????????????????????????)

By AA similarity criterion,

∆AOB ~ ∆COD

If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

\frac{\operatorname{area}(\triangle A O B)}{\text { area }(\Delta C O D)}=\left(\frac{A B}{C D}\right)^{2}

\frac{84}{\text { area }(\triangle C O D)}=\left(\frac{2 C D}{C D}\right)^{2}

area (\Delta \operatorname{COD})=12 \mathrm{~cm}^{2}

i

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