In triangle ABC, ad = 3bd, be = 2ec, AF = CF

In triangle ABC, ad = 3bd, be = 2ec, AF = CF

Even AE,
Because △ Abe and △ ace are equal height triangles
So s △ Abe / s △ ace = be / EC = 2
So s △ Abe / s △ ABC = 2 / 3
Similarly, s △ BDE / s △ Abe = 1 / 3
So s △ BDE = (2 / 9) s △ ABC
Similarly, s △ ECF = (1 / 6) s △ ABC
S△ADF=(3/8)S△ABC
So s △ def = (1-2 / 9-1 / 6-3 / 8) s △ ABC = (17 / 72) s △ ABC
The area of triangle DEF is 17 / 72 of triangle ABC

In the triangle ABC, D is the midpoint of AC, E F G is the quartering point of BC, and the area of the shaded triangle accounts for a fraction of the area of triangle ABC?
This triangle is the area of the bed connection

S△BED=1/4*S△BDC=1/2*1/4S△ABC=1/8S△ABC