Math CentralQuandaries & Queries


Question from Keith:
My question I thought was simple until I couldn’t find an answer anywhere.
I have a shape with lots of different curves and some straight lines.
I know how many feet the perimeter is and that’s it. How am I able to find
the square footage of an area if all I know is its perimeter length?


You can't (except in the trivial case in which the perimeter length is zero.) Consider a 3x1 rectangle and a 2x2 rectangle; they have the same perimeter length but different areas.

There is a result called the "isoperimetric inequality" that says that any shape with a given perimeter must have an area no greater than that of a disc with the same perimeter: A ≤ P2/(4 pi), and equality does not hold for any shape other than a disc.



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