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 $Δ C O D$ .

Open in App

Solution

ABCD is a trapezium in which, AB $∥$ CD and diagonals AC and BD intersect each other at O.
In $Δ A O B$ and $Δ C O D$ we have
$∠ 1 = ∠ 2$ [Alt $∠ s]$
$∠ 3 = ∠ 4$ [vert opp. \angle s\therefor \Delta AOB \sim \Delta COD$
[By AA criterion of similarity]
$\Rightarrow \frac{a r (Δ A O B)}{a r (Δ C O D)} = \frac{(2 C D)^{2}}{(C D)^{2}}$
[AB = 2CD (Given)]
$= \frac{4 C D^{2}}{C D^{2}} = 4$
$= \frac{84}{a r (Δ C O D)} = 4$ ;
$∴ a r (Δ C O D) = 84 + 4 = 21 c m^{2}$

Suggest Corrections

Similar questions

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.

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, 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)

Q. 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).

□ A B C D

is a trapezium,

A B ∥ D C

. Diagonals of trapezium intersect to each other at point

O

:
Area

(Δ A O B) = 3

sq. cm
Area

(Δ C O D) = 12

sq. cm
Area

(□ A B C D) =

_____

Join BYJU'S Learning Program

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

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 $Δ C O D$ .