How many laps around 21899 square feet will equal a mile?

Answer 1

1 mile = 5280 ft.

The shape with minimal perimeter for a given area is a circle. Thus:

For an area of 21899 sq ft, the perimeter (circumference) is:

2 x {pi} x sqrt(area / {pi}) ~= 524.6ft

Meaning:

laps ~= 5280 ft / 524.6 ft

~= 10.1 laps. (just over 10 laps)

If the area is a square field, then, for an area of 21899 sq ft, the perimeter is:

4 x sqrt(area) ~= 591.9 ft

Meaning:

laps ~= 5280 ft / 591.9 ft

~= 8.9 laps (just under 9 laps)

If the area is a rectangular field, 1 ft wide and 21899 ft long (having an area of 21899 sq ft), its perimeter is:

2 x (length + width) = 43800 ft

Meaning:

laps = 5280 ft / 43800 ft

~= 0.12 laps (just over a tenth of a lap).

In fact any number of laps less than about 10.1 laps can be given as the answer as the perimeter can be made to be any length over about 524.6 ft by selecting the shape of the 21899 square feet area as appropriate.

If the perimeter of the shape is a fractal, it can have infinite length (even though it encloses 21899 square feet) and so the number of laps will be as near to nothing as makes no odds (ie effectively zero laps).