ANSWER:
(c) 1/4ar (∆ ABC )
Since D is the mid point of BC, AD is a median of ∆ ABC and BE is the median of ∆ ABD.
We know that a median of a triangle divides it into two triangles of equal areas.
i.e., ar(∆ ABD ) = 1/2 ar(∆ ABC )
...(i)
⇒ ar(∆ BED ) = 1/2 ar(∆ ABD )
...(ii)
From (i) and (ii), we have:
ar(∆ BED ) = 1/2 ⨯ 1/2 ⨯ ar(∆ABC)
∴ ar(∆ BED ) = 1/4 ⨯ ar(∆ ABC )