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Actually, the resolution should not matter because these pictures are taken from an electron microscope and it already displays a bar scale of the real life size in micrometers.  All I have to do is go to Edit/Preferences/Units and Ruler and set the Ruler to pixels.  From there, I can draw a line using the ruler tool and line it up perfectly with the bar scale.  From there, I now have a pixel/micrometer conversion.   From the pixel count of the histogram, I should be able to convert it to micrometers using that pixel/micrometer conversion.  I just want to make sure the pixel units cancel out correctly.  That's what I am asking.

You were referring to calculating the printed area if I wanted to print out the image on paper.  For that, you need to use the resolution.  I am calculating the the surface area of the real-life cells.  This is totally different than the printed area on paper.

Also, I figured out what was wrong with the histograms.  Usually the measurements were accurate, but the random times were because of the cached histogram data.  Photoshop tells you when you should uncache the histogram data.  All I have to do is hit refresh and then it adjusts everything accordingly.  lol, I just wasn't aware you had to refresh anything so I never noticed the little exclamation point in the top corner of the histogram.