In a triangle `ABC`, `E` is the mid-point of median `AD`. Show that `a r\ (B E D)=1/4a r\ (A B C)```

Explanation

We know, the median of a triangle, divides the triangle into two triangles of equal areas.

So, in `Delta ABC`

`ar(ACD)=ar(ABD) = 1/2ar(ABC)->(1)`

Also, we are given,`E` is the mid-point of `AD` that means `BE` is the median of `Delta ABD`

So,

`ar(BED)=ar(AEB) = 1/2ar(ABD)`

From (1),

`ar(BED) = 1/2(1/2ar(ABC))`

...