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Answer:
Let ABC be a triangle and AD is the median of ΔABC
E is the mid point of AD
To prove : ar(BED)=
4
1
.ar(ABC)
In ΔABC,
ar(ABD)=ar(ACD) ___________ (1)
In ΔABD, BE is the median
ar(ABE)=ar(BED) __________ (2)
Now, ar(ABD)=ar(BED)
= 2. ar (BED) ______ (3)
ar(ABC)=ar(ABD)+ar(ACD)
ar(ABD)=2.ar(ABD) using (1)
ar(ABC)=2.2.ar(BED) - (2)
ar(ABC)= 4.ar (BED)
∴ar(BED)=
4
1
ar(ABC)
Hence it is proved.
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