Question

ABCD is a rectangle with O as any point in its interior. If $ar\left(△AOD\right)=3c{m}^2$ and $ar\left(△BOC\right)=6c{m}^2,$ then area of rectangle ABCD is

• A. $9c{m}^2$
• B. $12c{m}^2$
  
• C. $15c{m}^2$
  
• D. $18c{m}^2$
  

Answer 1

The correct option is D

$18c{m}^2$

In rectangle ABCD, O is any point. Also, $ar\left(△AOD\right)=3c{m}^{2}andar\left(△BOC\right)=6c{m}^2$
Join OA, OB, OC and OD

We know tht if O is any point in $ABCDthenar\left(AOB\right)+ar\left(COD\right)=ar\left(AOD\right)+ar\left(BOC\right)$
$=3+6=9c{m}^2$

$\therefore$ ar(rect. ABCD) $=2\times 9=18c{m}^2$