Question

The vertex A of $△ABC$ is joined to a point D on BC.If E is the midpoint od AD then ar($△BEC)$=?

(a) $\frac{1}{2}ar\left(△ABC\right)$

(b) $\frac{1}{3}ar\left(△ABC\right)$

(c) $\frac{1}{4}ar\left(△ABC\right)$

(d) $\frac{1}{6}ar\left(△ABC\right)$

Answer 1

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 )