You visited us 2 times! Enjoying our articles? Unlock Full Access!

Triangles on the Same Base (Or Equal Bases) and Equal Areas Will Lie between the Same Parallels

In the rectan...

Question

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( $△$ 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 ___ $c m^{2}$ .

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.

Q. ABCD is a rectangle with O as any point in its interior. If

a r (Δ A O D) = 3 c m^{2}

and

a r (Δ B O C) = 6 c m^{2},

then find area of rectangle ABCD.

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 $c m^{2}$ )

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]