Plat has several senses, one of which dates from the Middle English period and means a small patch of cultivated ground.
Yesterday morning was a sharp frost; and this had set the poor creatures to digging up their little plats of potatoes.
Rural Rides, by William Cobbett, 1832.
Some plats were extremely small: it was used on occasion for individual burial plots in a cemetery or for flower beds containing just a few plants. Plat also appeared as the second part of a compound who initial element signified what was grown in it: grass-plat, meadow-plat, corn-plat, flower-plat, fruit-plat. One that has survived longer than the others is hazel-plat, a term known in Kent for a plantation of hazel trees grown for their fruit.
Back in the spring, I spent a morning in a hazel plat, an orchard full of 100-year-old trees. It was a beautiful place, on a slope overlooking Plaxtol in Kent, and it reminded me of sitting in an Italian olive grove, surrounded by gnarled, dignified ancient trees.
Daily Telegraph, 21 Oct. 2006.
Plat is most probably a variant form of plot. The shift may have come about through a mental link to the adjective of the same spelling (from the French plat) that meant a flat area or more generally anything flat in nature, which is also the origin of our plate in the sense of the utensil we eat off. In a derived sense, plat could be a plan of an area of land, because it was itself flat. This has vanished from British usage, but plat remains current in the US for a map or diagram showing the boundaries of plots on a site.
The realtor’s plat shows it scarily subdivided into scores, even hundreds of quarter-acre parcels.
Once Upon a Time, by John Barth, 1994.