∵S△ABE=S△ADF
∴1/2AB*BE = 1/2AD*DF
∴AD/AB=BE/DF
又：AD/AB=3/2
∴BE/DF=3/2
令AD=3x,AB=2x；BE=3y,DF=2y,则有：
FC=DC-DF=AB-DF=2x-2y
EC=BC-BE=AD-BE=3x-3y
∵S△ABE=SAECF=S△AEC+S△ACF
∴1/2AB*BE=1/2EC*AB+1/2FC*AD
即：
1/2*2x*3y = 1/2*(3x-3y)*2x + 1/2*(2x-2y)*3x
y=2(x-y)
2x=3y
y = 2x/3
S△AEF=SAECF-S△ECF=S△ABE-S△EFC=1/2*AB*BE-1/2EC*FC
= 1/2*2x*3y-1/2(3x-3y)*(2x-2y)
= 1/2*2x*2x-1/2(3x-2x)*(2x-4x/3)
= 5²/3
SABCD=AB*AD=3x*2x=6x²
S△AEF/SABCD = 5²/3 /(6x²) = 5/18