ED is the median of ΔEBC.
∴area(ΔBED)=area(ΔECD).....(1)
BE is the median of ΔABD.
∴area(ΔBED)=area(BEA)…….(2)
CE is the median for ΔADC.
area(ΔECD)=area(ΔEAC)……(3)
i,e area(ΔBED)=area(ΔEAC) [ From (1)]……(4)
Now, area (ΔABC)=area(BEA)+area(ΔBED)+area(ΔECD)+area(ΔEAC)
area(ΔABC)=area(ΔBED)+area(ΔBED)+area(ΔBED)+area(ΔBED)[from(1),(2),(3) and (4)]
area(ABC)=4×area(ΔBED)
⇒area(ΔBED)=14ar(ΔABC)