What are your units? Square centimeters? Square kilometers? A pixel image does not know. You have to specify the spatial calibration. Do you know the size of your field of view, or of any object in your image, in real world units?
Regarding your update. No that's not correct. That will get you distance on the screen in cm, not mm (because there is 25.4 mm in an inch, not 2.54), and certainly not area in mm^2. You'd have to multiply by 25.4^2. Plus, o is a horrible letter to pick for a variable name - it looks too much like zero.
Do you want the real world area of your actual object that you took a picture of, or do you want the area that it takes up on your screen monitor?