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The Fencing Problem

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Introduction

The Fencing Problem A farmer has the need to enclose an area of land with 1,000 metres of fencing. He has to do so trying to make sure that he has enclosed the largest possible area of land. Therefore I will be investigating the shapes with the largest area that could be used to fence with 1000m of fencing. I will start by investigating different polygons. A polygon is a many sided shaped of strait lines which will be easy to measure, giving me more accurate results. These polygons will have a perimeter of 1000m. In this first section I will investigate the first set of polygons. Shape Equation Total area Perimeter Equilateral: 333.3+333.3+333.3 24,052� 1000�3= 333.3 288.64 x (333.3�2) ...read more.

Middle

The second shape of the polygon's family is the square: Shape Equation Total area Perimeter Quadrilateral: 250+250+250+250 62,500� 1000�4 250 x 250 = 62,500� To find the area of this square I have to: * Divide 1000 which is the perimeter by 3 which is the number of the polygon's sides * Multiply two of the polygon's sides By now I can see that between these polygons the square has the largest area. By the third shape, if this pattern is right the pentagon should have a larger area... But before continuing I will try two irregular polygons and investigate if by having different lengths of sides adding up to 1000m would affect the area. ...read more.

Conclusion

* Multiply the two shorter sides. I will have the area of a square so I divide it by 2 to make the area of an equilateral. Here I have proved myself wrong but I have stated something right: that irregular polygon's have smaller area than a regular polygon would have. With this investigation I have also shown again that the equilaterals have smaller area than the quadrilaterals. I have already shown the difference between irregular and regular polygons. I will continue investigating more areas of polygons and I think that as more lines the polygon has the larger the area. This document was downloaded from Coursework.Info - The UK's Coursework Database ?? ?? ?? ?? II ...read more.

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