# Q : 5    In Fig.$\small 9.33$, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that (iii) $\small ar(ABC)=2ar(BEC)$[Hint : Join EC and AD. Show that $\small BE\parallel AC$ and  $\small DE\parallel AB$, etc.]

ar($\Delta$ABC) = 4.ar($\Delta$BDE)   (in part 1)
and, ar($\Delta$BEC) = 2. ar($\Delta$BDE)  (in part ii )
$\Rightarrow$ ar($\Delta$ ABC) = 2. ar($\Delta$BEC)