Question

In a triangle ABC,E is the midpoint of median AD. Show that ar(BED)=1/4ar(ABC).

Answer 1

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Answer 2

given ad is median and e is the midpoint of ad,
therefore, 
ar(abd)= ar(adc)
=> ar(abc)= 1/2ar(abd)
                             ________________(i)
also e is the midpoint of ad.
therefore 
ar(bda)= 1/2 ar(bed)
                                _________________(ii)
from (I) and (II),
ar(bed)= 1/2*1/2ar(abc)
=> ar(bed)= 1/4 ar(abc)