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The Fencing Problem.  

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The Fencing Problem Target My target is to try and find a shape that will give a farmer the largest possible plot of land that can be enclosed with a 1200-meter perimeter fence. Hypothesis I have studied many shapes and decided that a circle will give the largest area. I have come to this conclusion because shapes like polygons are made up from a number of triangles, the number of triangle is equal to the number of sides. Therefore as you increase the number of sides you increase the number of triangles. A one sided shape would have no area at all; this therefore means that a circle should have the largest area as it has an infinite number of sides. My prediction is that the number of sides is relevant to the area as to say that the number of sides increases with the area, and visa versa. ...

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