Posted by **Sara** on Tuesday, January 10, 2012 at 11:19pm.

Suppose you have 100ft of fence to make a play area for your dog. Does a square or circle provide more area? What other factors might you take into consideration in designing your play area?

- Math -
**Reiny**, Tuesday, January 10, 2012 at 11:39pm
The circle is the most efficient shape for a maximum area given some perimeter.

Here is why:

if circumf = 100

2πr = 100

r = 100/(2π) = 15.915

area = πr^2 = π(15.915)^2 = 795.77

if you had a square:

each side = 25

Area = 25x25 = 625 which is quite a bit less than the circle

Any other shape, e.g. an equilateral triangle, is less than the area of a circle.

- Math -
**Alicia**, Tuesday, January 10, 2012 at 11:56pm
Circle it has a larger area by 3 more

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