<> Which CONSUMER model GPS receivers allow the user to walk around a property (closed loop) and calculate the area of the property?

Generally:  Early firmware versions may NOT have the ability to measure area.  Early G-12/G-12xl versions CANNOT be updated to obtain this feature.

As of February 2008

Garmin Colorado (all versions)
Garmin G-12
(late versions)
Garmin G-12xl (late versions)
Garmin VISTA  (all models)
Garmin LEGEND  (all models)
Garmin Venture (ver 2.26 and up)
Garmin G-48
Garmin G-60 (all models)
Garmin G-76  (all models)
Garmin G-V
Garmin GPS-176 (all models with latest firmware update)
Garmin GPS-276C
Garmin Rino (all models)

NOTE:  These are NOT survey grade instruments. However, the newer models have more accurate receivers than the older models.   Handheld GPS receivers have an instantaneous position accuracy in the clear and at rest of perhaps 3 to 10 meters (95% confidence).  When moving in wooded terrain, you can expect position excursion of 25/50/ and even hundreds of feet from the actual position depending on many factors very much inclusive of the density of the forest and the number of satellites in view at that moment.  My experience with a limited number of experiments is that you will get within perhaps 10% of the actual area on a good day.  If you need survey grade accuracy, then you must hire a surveyor.  None of the inexpensive GPS receivers can get you to the centimeter accuracy that some professional gear can attain under ideal conditions.