Area question , how to find the largest area

Question

What is the largest area we can enclose with a 120m fence. The fence is flexible and can be put it any shape.

Answer 1

Let's look at a few shapes:

1) Circle: Circumference = pi*D, then D =C/pi = 38.197 then the Circle Area = pi*D²/4 = 1145.9

2) Square: Each side would be 120/4 = 30, so the Area = 30² = 900

There is no need to check a rectangle because the optimal area rectangle is a square!

3) Equilateral Triangle: Each side = 120/3 = 40, the height of the triangle is H² + Base² = 40²

Then H = 34.64 So, the Triangle Area = 2(1/2)(20)(34.64) = 692.82

So you can see that the circle is the shape of maximum area!