How can I obtain the area (in square kilometers) inside a multipolygon? I drawed the boundaries of partidos inside Buenos Aires province, Argentina, and I want to compare the areas with the official numbers.

First you must know what coordinate system is used for calcutaling the official numbers. Then you need to get the geometry of the OSM polygon and calculate the area of it using the same coordinate system.

This query returns an area of one OSM polygon from a Spatialite database using the Finnish EPSG:3067 coordinate system. Native geometry (EPSG:4326 lat/lon coordinate) is converted into EPSG:3067 system before calculating the area.

select Area(Transform(GEOMETRY,3067))from multipolygons

where ogc_fid=19

=4126650.039729

I do not know what coordinate system the JOSM plugin is using when is calculates the areas but most probably it is not the same that is officially used in Argentina.