I have drawn a map in Inkscape. It looks like this:

Each shape has it's own outline and filling. Is it possible to - somehow - count the area of these shapes? If these shapes would be rectangular or circular I would be able to do so simply by getting the information of lengths of each sides / radius and count it... But in case of such complicated shapes how is it possible?
If its not possible to do so in Inkscape is there any program where you can count areas of shapes like in my drawing? I can imagine it is possible in some non-vector graphic program, where would be a tool - something like a magic wand - which would allow you to select the shape and it would count pixels inside of it. The question is: does this kind of program exist?
I will be really greatful for any help!