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7/7/02 The Fencing Problem Clare Dutton Question: A farmer has exactly 1000 metres of fencing and wants to fence of a plot of level land. She is not concerned about the shape of the plot, but it must have a perimeter of 1000m. So it could be anything with a perimeter (or circumference) of 1000m. She wishes to fence off the plot of land, which contains the maximum area. Investigate the shape, or shapes, that could be used to fence in the maximum area using exactly 1000m of fencing each time. Background work Before I look for the answer, I will do some trial investigations to determine a good way of investigating which shape gives the maximum area. Do regular or irregular shapes give a larger area? Triangle I know that the maximum area for an equilateral triangle (regular) is 48112.5224 m² (4.dp), by using 1/2 absinc. 1 side: 1000÷3=333? Area (A) = 1/2...

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