[bgjspxdr] 10 acres in a square furlong

one of the few places that multiples of 10 exist in U.S. customary units is obscure units of area:

10 square chain = acre
10 acre = square furlong

however, this feels awkward because 10 congruent squares cannot be arranged into a larger square.  it would have been nice if our counting system were based on a square number.

acre is a square with side length sqrt(10) ~= 3.162277660168379332 chain, or 0.3162277660168379332 furlong.

compare this with the metric system which does area in powers of 100: square meter, are, hectare, square kilometer, (megaare? megare?), (hectomegaare?), square megameter.  (but previously on sqrt(10) elsewhere in the metric system.)

64 square furlong in a square mile, realizable as an 8x8 array of square furlongs.  100 square chain in a square furlong.

partition a square into 10 congruent pieces.  10 strips, or a 2x5 array of rectangles, work.  are there any other ways?

an acre is a strip 1 chain by 10 chain (22 yard by 220 yard).

(a football field is (53 + 1/3) yard wide, or (2 + 14/33) chain.  including end zones, it has area (1 + 117/363) = (1 + 39/121) acre.  excluding end zones, (1 + 37/363) acre.)

partition a square into 10 regions of equal area, optimizing for compactness of the regions by some measure.