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Question

In the rectangle ABCD, O is any point inside the rectangle. If area( ΔAOD) = 30 cm2 and area( ΔBOC) = 60 cm2, area of the rectangle ABCD is

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(in cm2)

         


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(AOD)=12Area (APQD)Area (APQD)=60cm2Parallelogram PBCQ and triangle BOC are on same base BC and between same parallels.So, Area (BOC)=12Area (PBCQ)Area (PBCQ)=120cm2Area (ABCD)=Area (APQD)+Area (PBCQ)=180cm2 

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