Question

In rhe figure, ABCD and FECG are parallelograms equal in area. IF $ar\left(△AQE\right)=12c{m}^2,thenar\left(||gmFGBQ\right)$ =

• A. $12c{m}^2$
  
• B. $20c{m}^2$
  
• C. $24c{m}^2$
  
• D. $36c{m}^2$
  

Answer 1

The correct option is C

$24c{m}^2$

In the figure, ABCD and EFCG are prallelograms equal in area and $\left(△AQE\right)=12c{m}^2$
IN ||gm AQED, AE is the diagonal
$\therefore ar\left(△AQE\right)=\frac{1}{2}ar\left(||gmAQED\right)\Rightarrow 12c{m}^2=\frac{1}{2}ar\left(||gmAQED\right)\therefore ar\left(||gmAQED\right)=24c{m}^2\because ar\left(||gmABCD\right)=ar||gmFECG\Rightarrow ar\left(||gmAQED\right)+ar\left(||gmQBCE\right)=ar\left(||gmQBCE\right)+ar\left(||GmFGBQ\right)\Rightarrow ar\left(||gmAQED\right)=ar\left(||gmFGBQ\right)=24c{m}^2$