The Total solution for NCERT class 6-12
In a triangle ABC, E is the mid-point of median AD. Show that ar(BED)= ¼ ar(ABC).
ar(BED) = (1/2)×BD×DE
Since, E is themid-point of AD,
AE = DE
Since, AD is themedian on side BC of triangle ABC,
BD = DC,
DE = (1/2) AD — (i)
BD = (1/2)BC — (ii)
From (i) and (ii), weget,
ar(BED) =(1/2)×(1/2)BC × (1/2)AD
⇒ ar(BED) =(1/2)×(1/2)ar(ABC)