In the rectangle ABCD, O is any point inside the rectangle. If area (ΔAOD) = 30 $c m^{2}$ and area (ΔBOC) = 60 $c m^{2}$ , then find the area of the rectangle ABCD.

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Solution

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

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