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Question: A farmer has exactly 1000 metres of fencing, with it she wishes to fence off a plot of level land. She is not concerned about the shape of the plot, but it must have a perimeter of 1000 metres. What she does wish to do is fence off the plot of land, which contains the maximum area. The answer is a circle but in this course work I will try to explain why. All numbers will be rounded to 2 decimal places. Regular polygons have the largest areas This shows that the closer the values of the height and width the larger the area. I made many more of these calculations and created a graph. This graph reinforces that 250 x 250 is the rectangle with the largest area which shows that the shapes with the largest area are those with equal sides. Number of Sides Area 3 48111.11 4 62500 5 68800 6 72168.72 7 73890.13 8 75444.17 9 76318.81 10 76942.09 Conclusion Regular polygons have larger areas than irregular...

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