



 
Keith, 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 ≤ P^{2}/(4 pi), and equality does not hold for any shape other than a disc. RD
 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 