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Question:

In a triangle ABC, E is the mid-point of median AD. Show that area(BED) = 1/4 area(ABC).

Solution:

ADis the median onBCofΔABC...Given∴A(ΔABD)=A(ΔACD).andA(ΔABD)=A(ΔACD)=12A(ΔABC)(1)EBis the median on AD ofΔABD...Given∴A(ΔBED)=A(ΔBEA).andA(ΔBED)=A(ΔBEA)=12A(ΔABD)(2)From (1) and (2),A(ΔBED)=12×12A(ΔABC)A(ΔBED)=14A(ΔABC)[henceproved]