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In triangle ABC, D is the midpoint of BC and E is the midpoint of AD. The line through these points splits the triangle. ar(BED) compared to ar(ABC):

Class 9Areas — Figures on the Same BaseGeometry

A $\frac{1}{4}$
B $\frac{1}{2}$
C $\frac{1}{3}$
D $\frac{1}{6}$

Step-by-Step Solution

Median AD gives ar(ABD) =

\frac{1}{2}

ar(ABC). In triangle ABD, BE is the median to AD, so ar(BED) =

\frac{1}{2}

ar(ABD) =

\frac{1}{4}

ar(ABC).

Answer: A)

\frac{1}{4}

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