Context :

Aims : We determine the age , metallicity and initial mass function of three clusters , namely NGC~265 , K~29 , NGC~290 , located in the main body of the Small Magellanic Cloud .
In addition , we derive the history of star formation in the companion fields .

Methods : We make use of ACS/WFC HST archive data .
For the clusters , the age and metallicity are derived fitting the integrated luminosity function with 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 .

Results : For the clusters we find the following ages and metallicities : NGC~265 has log ( Age ) = 8.5 \pm 0.3 yr and metallicity 0.004 \pm 0.003 ( or [ Fe/H ] =-0.62 ) ; K~29 has log ( Age ) = 8.2 \pm 0.2 yr and metallicity Z= 0.003 \pm 0.002 ( or [ Fe/H ] =-0.75 ) ; NGC~290 has log ( Age ) = 7.8 \pm 0.5 yr and metallicity 0.003 \pm 0.002 ( or [ Fe/H ] =-0.75 ) .
The superior quality of the data allows the study of the initial mass function down to M \sim 0.7 M _ { \odot } .
The initial mass function turns out to be in agreement with the standard Kroupa model .
The comparison of the NGC~265 luminosity function with the theoretical ones from stellar models both taking overshoot from the convective core into account and neglecting it , seems to suggest that a certain amount of convective overshoot is required .
However , this conclusion is not a strong one because this cluster has a certain amount of mass segregation which makes it difficult to choose a suitable area for this comparison .
The star formation rate of the field population presents periods of enhancements at 300-400 Myr , 3-4 Gyr and finally 6 Gyr .
However it is relatively quiescent at ages older than 6 Gyr .
This result suggests that at older ages , the tidal interaction between the Magellanic Clouds and the Milky Way was not able to trigger significant star formation events .

Conclusions :