Q

# D, E and F are respectively the mid-points of the sides BC, CA and AB of a ∆ ABC. Show that (iii) ar (BDEF) = 1/2 ar (ABC)

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) $\small ar(BDEF)=\frac{1}{2}ar(ABC)$

Views

ar($\Delta$DEF) = ar ($\Delta$ BDF).........(i)

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

Hence proved.

Exams
Articles
Questions