You can always add more perimeter, so you want a lower bound on the perimeter given the area. The isoperimetric inequality (https://en.wikipedia.org/wiki/Isope

You can always add more perimeter, so you want a lower bound on the perimeter given the area. The isoperimetric inequality (https://en.wikipedia.org/wiki/Isoperimetric_inequality https://en.wikipedia.org/wiki/Isoperimetric_inequality) says that the smallest perimeter for a given area is that of a circle.