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The Fencing Problem

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Introduction

The Fencing Problem I am writing this investigation for a farmer who has 1000m2 of fencing and wants to find out how he can create the most area by using the fencing and rearranging the fence in different shapes. From only 3 sides to 99999 sides I have worked out the highest and lowest area for the farmers plot of land. ...read more.

Middle

(500-500) (500-300) =5916.079 Area = 500(500-400) (500-400) (500-200) =38729.833 Area = 500(500-450) (500-450) (500-150) =20916.501 Now I will try a different family of shapes a 4 sided shape but I think that the greatest area of a shape will come from a regular shape. Area = 250 x 250 = 62,500m2 Area = 200 x 300 = 60,000m2 Area = 150 x 350 = 52,500m2 Area = 100 x 400 = 40,000m2 Area = 50 ...read more.

Conclusion

I will now increase the number of sides on a shape and see if I can find a maximum area. I can see that as the number of sides increase the area also increases. The question now is does a circle have infinity sides, 1 single side or a peak number of sides n- sided Area = This formula shows that as n increases to infinity approaches tan 90 so that the angle between adjacent sides becomes 2x 90= 180o thus giving a circle. For a circle of a radius r = ...read more.

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