I have 200m of fencing and I am trying to get the largest area with that amount of fencing

Guest Aug 16, 2017

The max area is always a square:


P = 200, s = 200/4 = 50, A = 50*50 = 2500 square meters.

Mathhemathh  Aug 16, 2017

No,the max area is always a circle.(And the  the max volume enclosed by min surface area is always a sphere.)

Fence length  = 200 metres      which can enclose a circular area of


pi (r^2).                 So find r,the radius.

Circumference  = 200   =  2 pi(r)     

pi (r)                 =100


radius  is  100/(pi)         Area is  pi   X { (100)^2} /(pi^2) }

                                      Area = (100^2)  /pi      = 3183.098   which is greater than the area of the square.


The most area efficient shape is a circle.  The most volume efficient shape is a sphere.That's why planets are not cube shaped.

frasinscotland  Aug 16, 2017


The guest is correct......a circle will give us the greatest area



cool cool cool

CPhill  Aug 16, 2017
edited by CPhill  Aug 16, 2017

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