Thanks for the input Greg. In defence of my attack at NI help: my search of the NI website Product Manuals found no entry for Equivalent Rect, and the VBAI help was useless.
Technically, a Rectangle with the Same Perimeter and Area could take on many forms, surely? maybe not... Anyway, as with yourself, I get nonsense back occasionally, so have avoided its use.
I'm now determining the Perimeter and Area from the Particle tool, and checking they are both within my limits. This seems to work well enough, although I'm not entirely satisfied that I'm excluding all other rectangle shapes

Agreed, if I could somehow determine the orientation, place a new coordinate system at the bottom left corner and caliper the height in y and width in x I'd be onto a winner. I'm not so sure where to start with that though...

Thanks for your assistance! I'd rate your answer, but I don't have enough privileges yet to rate anyone

Cheers,
Thoric (CLA, CLED, CTD and LabVIEW Champion)