Vector and raster size differ wildly

[nk027]

Even after projecting the shapefile (long-lat areas are only estimates) the calculated area is partly significantly (>10% ) smaller than the area implied by the amount of contained pixels.

This is due to the fact that while MOD13Q1 is supposed to have a pixel size of 250m^2 it actually seems to be 231.6564m^2 (according to the raster package and QGIS). After accounting for that the areas match very closely (+/- 1%).