∵△ABD和△BC等底
∴做高AN,CM,那么高比:AN/CM=9/24=3/8,即AN=3/8CM
∵BE/CE=DF/CF=1/2,那么BD∥EF,MH/CH=1/2,MH=1/3CM
∴AN/MH=(3/8CM)/(1/3CM)=9/8
∵BD∥EF
∴AK/FK=9/8,即AK/AF=9/17
∴KG/EF=9/17
EF/BD=2/3(CF/BC=2/3)
∴KG=9/17EF=9/17×2/3BD=6/17BD
∴S△AFG=6/17S△ABD=6/17×9=54/17
∵△AFG∽△AEF
∴S△AFG/S△AEF=(AK/AF)²=(9/17)²
∴S△AEF=(17/9)²S△AFG=17²/9²×54/17=34/3