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?

Minimum area, as stated in an earlier post, would be zero. A line 66 cm long, zero width (66 * 2 = 132).
Maximum area is a circle. For the equations...
(pi)d=132. So d = 132/pi. d=42.0169
r=d/2. r=21.00845
(pi)r^2=area.
Area = 1386.55 cm^2.

As for proof, the best proof I can come up with for this being the highest area is to compare to the line, a rectangle, and a square. The line has zero area. A rectangle 50x16 would have an area of 800 cm^2. A square (33x33) would have an area of 1089 cm^2. Out of these, the circle is the biggest. This may not prove that the circle has the largest possible area, but I don't feel like doing the research for the proper proof.

Posted by Half-Mad on 2002-06-03 19:07:14