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Here's a quick summary of the results presented thusfar in this thread, as well as some mathematically accurate computed areas:

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Other than the two very odd initial entries from the OP, all the other area estimates have been clustered within 1 or 2% of the true, mathematically computed value.  Given that PS is a pixel based program and hence, it can only do placements and measurements accurate to the number of pixels (eg, 1 pixel out of 100 in diameter = 1%), and the fractional error in the area becomes twice the fractional error in the diameter (because it is squared), all in all, I think PS is doing a very reasonable job.   If the OP needs more accuracy and wants to stick with this method, then the only way to get more accurate numbers is to let the features of interest be larger than 100 pixels.

Personally, remembering previous threads about this problem, I strongly suspect that vastly larger errors will be introduced by shadowing and incorrect inclusion / exclusion in the selection of the features of interest, not limitations of the integer math involved.

Tom M