In the rectangle ABCD, O is any point inside the rectangle. If area( ΔAOD) = 30

Question

c m^{2}

and area( ΔBOC) = 60

c m^{2}

, area of the rectangle ABCD is
___
(in

c m^{2}

)

Answer:
:

Draw a line through O parallel to A D as shown. Parallelogram A P Q D and triangle A O D are on same base A D and between same parallels. So, Area (A O D) = \frac{1}{2} Area (A P Q D) Area (A P Q D) = 60 c m^{2} Parallelogram P B C Q and triangle B O C are on same base BC and between same parallels. So, Area (B O C) = \frac{1}{2} Area (P B C Q) Area (P B C Q) = 120 c m^{2} Area (A B C D) = Area (A P Q D) + Area (P B C Q) = 180 c m^{2}

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