# Math

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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 -

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

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 -

Circle it has a larger area by 3 more

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