# Q: 5    D, E and F are respectively the mid-points of the sides BC, CA and AB of a $\small \Delta ABC$. Show that          (iii) $\small ar(BDEF)=\frac{1}{2}ar(ABC)$

M manish

ar($\Delta$DEF) = ar ($\Delta$ BDF).........(i)
So, ar(||gm BDEF) = ar($\Delta$BDF) + ar ($\Delta$DEF)
= 2 . ar($\Delta$DEF)    [from equation (i)]
$\\= 2[\frac{1}{4}ar(\Delta ABC)]\\ =\frac{1}{2} ar(\Delta ABC)$