In the rectangle ABCD, O is any point inside the rectangle. If area( $△$ AOD) = 30 $c m^{2}$ and area( $△$ BOC) = 60 $c m^{2}$ , Find the area of the rectangle ABCD. [2 MARKS]

Open in App

Solution

Concept : 1 Mark
Calculation : 1 Mark

Draw a line through O parallel to AD as shown .

Parallelogram APQD and triangle AOD are on same base AD and between same parallels.

So,ar( $△$ AOD) = $\frac{1}{2}$ ar(APQD)

ar(APQD) = 60 $c m^{2}$

Parallelogram PBCQ and triangle BOC are on same base BC and between same parallels.

So, ar( $△$ BOC)= $\frac{1}{2}$ ar(PBCQ)

ar(PBCQ) = 120 $c m^{2}$

ar(ABCD) = ar(APQD) + ar(PBCQ) = 180 $c m^{2}$

Suggest Corrections

Similar questions

In the rectangle ABCD, O is any point inside the rectangle. If area( ΔAOD) = 30 $c m^{2}$ and area( ΔBOC) = 60 $c m^{2}$ , area of the rectangle ABCD is

___

(in $c m^{2}$ )

In the rectangle ABCD, O is any point inside the rectangle. If area (ΔAOD) = 30 $c m^{2}$ and area (ΔBOC) = 60 $c m^{2}$ , find the area of the rectangle ABCD.

In the rectangle ABCD, O is any point inside the rectangle. If area( $△$ AOD) = 30 $c m^{2}$ and area( $△$ BOC) = 60 $c m^{2}$ , Find the area of the rectangle ABCD. [2 MARKS]

In the rectangle ABCD, O is any point inside the rectangle. If area( ΔAOD) = 30 $c m^{2}$ and area( ΔBOC) = 60 $c m^{2}$ , area of the rectangle ABCD is ___ $c m^{2}$ .

Q. ABCD is a rectangle of area

40 c m^{2}

. If X is any point on AB, what is the area of

Δ X C D

Join BYJU'S Learning Program

In the rectangle ABCD, O is any point inside the rectangle. If area(△AOD) = 30 cm2 and area(△BOC) = 60 cm2, Find the area of the rectangle ABCD. [2 MARKS]

In the rectangle ABCD, O is any point inside the rectangle. If area( $△$ AOD) = 30 $c m^{2}$ and area( $△$ BOC) = 60 $c m^{2}$ , Find the area of the rectangle ABCD. [2 MARKS]