Solution:
ar(BED) = (1/2)×BD×DE
Since, E is the mid-point of AD,
AE = DE
Since, AD is the median on side BC of triangle ABC,
BD = DC
,
DE = (1/2) AD — (i)
BD = (1/2)BC — (ii)
From (i) and (ii), we get,
ar(BED) = (1/2)×(1/2)BC × (1/2)AD
⇒ ar(BED) = (1/2)×(1/2)ar(ABC)
⇒ ar(BED) = ¼ ar(ABC)
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