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.

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Solution

Draw a line through O parallel to ADas shown.

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

So, Area of parallelogram APQD = 2 x Area of AOD

Area of APQD = $60 c m^{2}$

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

So, Area parallelogram PBCQ = 2 x Area BOC

Area of PBCQ = $120 c m^{2}$

Area of ABCD = $Area (A P Q D) + Area (P B C Q) = 180 c m^{2}$

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