I see a couple have looked at this your so quick I should have mentioned what the upshot of looking at the area of a circle with a Scottish miles being the diameter and the old Egyptian value for pi used 3.1604.... 640 acres.

I am pretty sure but havn't doubled checked 640 acres may have been called a 'hide'.

In any case 640 acres is a square mile 5280 x 5280 / 43560 = 640 acres in number at least, and so the area of the circle (Scottish) equals the area of the square.

Jim