What is the maximum area that could be enclosed by a piece of string 132 cm long? What shape would that area take?

What is the minimum area that could be enclosed by the same string? What shape will it take?

(In reply to re(2): Solution by levik)

You may be on the right path. We can show that it must be a convex polygon. If there is any concavity, drawing a line across it will produce a new convex polygon with a larger area and a smaller perimeter. Constructing a polygon similar to this new polygon but with the 132cm perimeter will result in enclosing even more area.

Posted by TomM on 2002-06-07 16:41:20