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 , area of the rectangle ABCD is ___ (in c m 2 ) <img class="img-thumbnail" style="display: block;" alt="In The Rectangle ABCD, O Is Any Point Inside The Rectangle. ..." title="Click to Enlarge Image" class="img-thumbnail" alt="Click to Enlarge Image" title="Click to Enlarge Image" alt="" height="198" src="https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/50321_f0698afc4784f85d6645dc933bd7fe77eebeee1120160630-5020-arpfcr.png" width="324"> Options:

Answer: Option A : 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 ) = 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 ) = 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

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

Question

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

___

(in $c m^{2}$ )

Options:

Answer: Option A
:

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