We recover the spatially resolved star formation history across the entire main body and Wing of the Small Magellanic Cloud (SMC), using fourteen deep tile images from the VISTA survey of the Magellanic Clouds (VMC), in the YJKs filters. The analysis is performed on 168 subregions of size 0.143 deg2, covering a total contiguous area of 23.57 deg2. We apply a colour-magnitude diagram (CMD) reconstruction method that returns the best-fitting star formation rate SFR(t), age--metallicity relation, distance and mean reddening, together with their confidence intervals, for each subregion. With respect to previous analyses, we use a far larger set of VMC data, updated stellar models, and fit the two available CMDs (Y-Ks versus Ks and J-Ks versus Ks) independently. The results allow us to derive a more complete and more reliable picture of how the mean distances, extinction values, star formation rate, and metallicities vary across the SMC, and provide a better description of the populations that form its Bar and Wing. We conclude that the SMC has formed a total mass of (5.31+-0.05)x10^8 Msun in stars over its lifetime. About two thirds of this mass is expected to be still locked in stars and stellar remnants. 50 per cent of the mass was formed prior to an age of 6.3 Gyr, and 80 per cent was formed between 8 and 3.5 Gyr ago. We also illustrate the likely distribution of stellar ages and metallicities in different parts of the CMD, to aid the interpretation of data from future astrometric and spectroscopic surveys of the SMC.
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