设DE=x,CF=y,EF=zz
则2[z/(x+z)+(z^2)/(x^2)*x/(x+z)]=160/16=10⇒z/x=5
2[z/(y+z)+(z^2)/(y^2)*y/(y+z)]=160/24=20/3⇒z/y=10/3
设z=10t,x=2t,y=3t
则AB=EF=10t,CF=3t,DE=2t,
∴OB/OD=AB/CD=2/3,OB/BD=2/5
∴S[△AOB]/S[平行四边形ABFE]=S[△AOB]/2S[△ABE]
=S[△AOB]/2S[△ABD]=OB/2BD=1/5
∴S[△AOB]=S[平行四边形ABFE]/5=32