解：∵?$\frac {AE}{EC}=\frac {1}{2}$?
∴?$\frac {AE}{AC}=\frac {1}{3}$?
∵?$DE∥BC$?
∴?$∠DEO=∠OBC，$??$∠EDO=∠OCB$?
∴?$△DOE∽△COB$?
∴?$\frac {DE}{BC}=\frac {AE}{AC}=\frac {1}{3}$?
∴?$\frac {{C}_{△DOE}}{{C}_{△BOC}}=\frac {DE}{BC}=\frac {1}{3}，$??$\frac {{S}_{△DOE}}{{S}_{△BOC}}={(\frac {DE}{BC})}^2={(\frac {1}{3})}^2=\frac {1}{9}.$
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