1.

In the figure, CD, AE and BF are one-third of their respective sides. It follows that `AN_2 : N_2 N_1 : N_1 D= 3 : 3 : 1` and similarly for lines BE and CF. Then the area of triangle `N_1 N_2 N_3`. in term of`Delta ABC` is

Answer» `AE=1/3AC``area(/_ABE)=1/3area(/_ABC)`
`area(/_ABN)=6/7area(/_ABC)`
`=6/7*1/3area(/_ABC)`
`=2/7 area(/_ABC)`
`area(/_BFC)=1/3(/_ABC)`
`area(BNC)=6/7area(/_BFC)`
similarly,
`area(/_BNC)=2/7area(/_ABC)`
`area(ANC)=2/7area(/_ABC)`
`area(N_1N_2N_3)=area(ABC)-3(2/7area(ABC))`
=`area(ABC)/7`.


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