AD is the median of ΔABC.
Therefore, it will divide ΔABC into two triangles of equal area.
Area ΔABD = Area ΔACD
∴area(ΔABD)=12area(ΔABC) ------------(1)
In ΔABD, E is the mid-point of AD.
Therefore, BE is the median.
Then Area ΔBED = Area ΔABE
∴area(ΔABE)=12area(ΔABD) ------------(2)
area(ΔABE)=12×12area(ΔABC)
area(ΔABE)=14area(ΔABC)...........................(3)
In ΔADC, E is the mid-point of AD.
Therefore, EC is the median.
Area ΔAEC = Area ΔCED
∴area(ΔACE)=12area(ΔADC)
area(ΔACE)=12×12area(ΔABC)
area(ΔACE)=14area(ΔABC)....................(4)
From (3) and (4) we get
area(ΔABE)=area(ΔACE)
![711649_569732_ans_146d59f522e746b5a4edbdcd3149381e.png](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/711649_569732_ans_146d59f522e746b5a4edbdcd3149381e.png)