From a practical standpoint, you may have heard that a sphere encloses a volume with minimal surface area. That implies that it's possible to have a volume enclosed with larger surface areas. That implies that in 2D, we can have a minimum area enclosure (i.e. a circle), which then implies that there are other examples of larger perimeter.
There was a math problem/proposal that I once read, which challenged the reader to give the minimum area needed to turn a line segment around 180 degrees. The first answer that comes to mind would be a circle of the segment's diameter. Closer examination (based upon the 0-width of the line segment) proves that the minimum area is 0 ... since you can move the line segment back and forth with an infinitesimal swing of arc. The resulting "polygon" looks like a star with infinite spikes of 0 width. As you can imagine, the perimeter is infinite, too. Fascinating stuff, although a bit mentally masturbatory.