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A square mile is 640 acres, so indeed 1/2 mile x 1/2 mile is 160 acres.
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The Math is not your friend, Spacecoast.
1/2 of 640 is 320.
I grew up in open farm county..... a field or pasture was "a section", "a 1/2", "a quarter", "an 80", or "that little strip/scrap"..... a "quarter" is 160 acres, or 1/4 of a section, which is a square mile, 640 acres.