| By analyzing an e+e-annihilation data sample of 2.93 fb-1 collected at the center-of-mass energy of 3.773 GeV with the BESⅢ detector,we have measured the absolute branching fractions of fourteen multibody hadronic D decays to η(D→ηX).The branching fractions measured in the unit of 10-4 are listed as:B(D0→K-π+η)=185.3±2.5±3.1,B(D0→KS0π0η)=100.6 ± 3.4 ± 3.1,B(D0→K+K-η)=0.6±0.2 ± 0.1,B(D0→KS0KS0η)=1.3 ± 0.6 ± 0.2,B(D0→K-π+π0η)=44.9±2.2±1.5,B(D0→KS0π+π-η)=28.0 ± 1.9 ± 1.0,B(D0→KS0π0π0η)=17.6±2.3 ± 1.4,B(D0→π+π-π0η)=32.3±1.7 ± 1.4,B(D+→KS0π+η)=130.9 ± 3.7 ± 3.1,B(D+→KS0K+η)=1.9 ± 0.5 ± 0.1,V(D+→K-π+π+η)=13.5±1.1±0.4,B(D+→KS0π+π0η)=12.2±2.4±0.6,B(D+→π+π+π-η)=34.1±1.7 ± 1.2,B(D+→π+π0πη0η)=32.0±2.8 ± 1.7,where the first and second uncertainties are statistical and systematic,respective-ly.Compared to the previous measurements reported in Particle Data Group,the B(D0→KS0π0η)is determined with much bettter precision while the other decays are measured for the first time.In addition,for the decays D0→K-π+η,KS0π0η,K-π+π+π0η,π+π-π0ηand D+→KS0π+η,π+π+π-η,we have measured the branching fraction asym-metries for these decays and their corresponding charged conjugate decays,no evidence of significant CP violation is found. |