In an 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) = 84 cm². Find ar(∆COD).

Open in App

Solution

In ∆AOB and ∆COD, we have:

$∠ A O B = ∠ C O D (Vertically opposite angles) ∠ OAB = ∠ OCD (Alternate angles as AB ∥ CD) Applying AA similiarity criterion, we get : △ AOB ~ △ COD ∴ \frac{a r (△ A O B)}{a r (△ C O D)} = \frac{A B^{2}}{C D^{2}} \Rightarrow \frac{84}{a r (△ C O D)} = {(\frac{A B}{C D})}^{2} \Rightarrow \frac{84}{a r (△ C O D)} = {(\frac{2 C D}{C D})}^{2} \Rightarrow a r (△ C O D) = \frac{84}{4} = 21 {cm}^{2}$

Suggest Corrections

Similar questions

Q. In a trapezium ABCD, it is given that AB∥CD and AB = 2 CD. Its diagonals AC and BD intersect at a point O such that ar(△AOB) = 84 cm²
Find ar(△COD)

Ina trapezium ABCD, it is given that AB || CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that ar $(Δ A O B) = 84 c m^{2}$ . Find ar $(Δ C O D)$ .

Q. In a trapezium ABCD, O is the point of intersection of AC and BD, AB ∥ CD and AB = 2 × CD. If area of AOB = 84 cm², find the area of ΔCOD.

Q. In a trapezium ABCD, O is the point of intersection of AC and BD, AB

∥

CD and

A B = 2 C D

. If the area of

Δ A O B = 84 c m^{2}

, find the area of

Δ C O D

Q. In quadrilateral

A B C D

, diagonals

A C

and

B D

intersect at point

E

such that

A E : E C = B E : E D

.
Show that:

A B C D

is a trapezium.

Join BYJU'S Learning Program

In an 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) = 84 cm2. Find ar(∆COD).

In ∆AOB and ∆COD, we have: ∠AOB = ∠COD (Vertically opposite angles)∠OAB = ∠OCD (Alternate angles as AB ∥ CD)Applying AA similiarity criterion, we get:△AOB~△COD∴ ar(△AOB )ar(△COD) = AB2CD2⇒ 84ar(△COD) = ABCD2⇒ 84ar(△COD) = 2CDCD2⇒ ar(△COD) = 844 = 21 cm2

In an 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) = 84 cm². Find ar(∆COD).