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We determine the age, metallicity and initial mass function of threeclusters, namely NGC 265, K~29, NGC 290, located in the main body of the SmallMagellanic Cloud. In addition, we derive the history of star formation in thecompanion fields. We make use of ACS/WFC HST archive data. For the clusters,the age and metallicity are derived fitting the integrated luminosity functionwith single synthetic stellar population by means of the $\chi^2$ minimization.For the companion fields, the history of star formation is derived using the$\chi^2$ minimization together with the downhill-simplex method.For theclusters we find the following ages and metallicities: NGC 265 haslog(Age)=$8.5\pm0.3$ yr and metallicity $0.004\pm0.003$(or [Fe/H]=-0.62);\object{K~29} has log(Age)=$8.2\pm0.2$ yr and metallicity Z=$0.003\pm0.002$ (or[Fe/H]=-0.75); NGC 290 has log(Age)=$7.8\pm0.5$ yr and metallicity$0.003\pm0.002$(or [Fe/H]=-0.75). The superior quality of the data allows thestudy of the initial mass function down to M$ \sim$ 0.7 M$_\odot$. The initialmass function turns out to be in agreement with the standard Kroupa model. Thecomparison of the NGC 265 luminosity function with the theoretical ones fromstellar models both taking overshoot from the convective core into account andneglecting it, seems to suggest that a certain amount of convective overshootis required. The star formation rate of the field population presents periodsof enhancements at 300-400 Myr, 3-4 Gyr and finally 6 Gyr. However it isrelatively quiescent at ages older than 6 Gyr. This result suggests that atolder ages, the tidal interaction between the Magellanic Clouds and the MilkyWay was not able to trigger significant star formation events.Comment: 20 pages. A&A accepte

Three clusters of the SMC from ACS/WFC HST archive data: NGC 265, K 29 and NGC 290 and their field population