That was the final result of the original place I found the question. The coastline problem.
Thinking about this, the area wouldn’t be that difficult at all (which is what L.J. King ‘s idea may work for) and yet because of the vast number of possible configurations of shape – including (and especially) the seemingly fractal nature of “edge” when land touches water… perimeter becomes an impossible task to get precisely correct – or even an estimate of.
Still, here’s a question: What about “reasonable estimate” based upon need?
For example, if you’re planning to walk the island perimeter, a “rough circle” around the island should be possible to estimate, shouldn’t it?
The stride of a human is approximately 30 inches, so the granularity of the estimation becomes much easier to handle.