The Total solution for NCERT class 6-12
In a triangle ABC, E is the mid-point of median AD. Show that ar(BED)= ┬╝ ar(ABC).
ar(BED) = (1/2)├ЧBD├ЧDE
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 тАФ (i)
BD = (1/2)BC тАФ (ii)
From (i) and (ii), weget,
ar(BED) =(1/2)├Ч(1/2)BC┬а├Ч┬а(1/2)AD
тЗТ┬а ar(BED) =(1/2)├Ч(1/2)ar(ABC)