You need to find out how big one pixel is, in appropriate units, and then multiply by the number of pixels you have identified.
If you are working with a JPEG image, chances are that you will not have accurate information stored in the original file necessary to calculate the real-world size of the pixels. If you are using something designed specifically as a scientific instrument, then the information might be there in a JPEG image. Also, some models of high-end cameras store auto-focus distance and aperture information that can be used to estimate real-world sizes -- for example not even all Canon DSLRs will have that information.
Note: the "Resolution" EXIF information that is stored with JPEG images is more likely to be garbage than not.
If you are working with an image that was originally recorded directly as a TIFF or PNG file, the probability goes up that meaningful information is stored with the file.
If you are working with an image that was originally recorded as a DICOM image, then chances are quite good that the DICOM headers have the detailed information you need to calculate the pixel area.
