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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]

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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 $c m^{2}$

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