I have few problems understanding how units are managed in QGIS. According to the area column I created for a shapefile, the area of a shape is 0.7727... I just checked on Wikipedia and indeed the area of the region is 7,727 km2. So in which unit is the area column expressed? It was my understanding that because my projection was WSG84 all the units are in meters, so why my column doesn't say 7.727×10^9?
If your layer's CRS is WGS84 (EPSG:4326), the layer units are in degrees. You can check this by examining the CRS definition string in the layer selection dialog.
To calculate area in meters, you have to reproject the layer to some suitable CRS for your region of interest. One default option is to go for a UTM zone that covers your area.