# Q : 2      In a triangle ABC, E is the mid-point of median AD. Show that     $\small ar(BED)=\frac{1}{4}ar(ABC)$.

M manish

We have a triangle ABC and  AD is a median. Join B and E.

Since the median divides the triangle into two triangles of equal area.
$\therefore$ ar($\Delta$ABD) = ar ($\Delta$ACD) = 1/2 ar($\Delta$ABC)..............(i)
Now, in triangle $\Delta$ABD,
BE is the median [since E is the midpoint of AD]
$\therefore$ ar ($\Delta$BED) = 1/2 ar($\Delta$ABD)........(ii)

From eq (i) and eq (ii), we get

ar ($\Delta$BED) = 1/2 . (1/2 ar(ar ($\Delta$ABC))
ar ($\Delta$BED)  = 1/4 .ar($\Delta$ABC)

Hence proved.

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