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I have suggested for the game I play in that each existing hex be subdivided into 7 smaller hexes for the purposes of building a kingdom.
Stating that the only function possible to get from an area of 374 sq miles is one single farm is stretching it. A lot. (If one line is 12 miles long).
Most medieval farms were more in the order of a mile or two in area.
FYI-- It's been mentioned elsewhere, but it isn't one farm, it's a hex dedicated to farming, which would include many farms and farmland in that hex, as well as whatever else would be needed for such. Unless you wish to think of it as one farm and subdivide, you need not do so, just assume that the hex contains a bunch of farms and the people to work them. :)