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I will be investigating the shape, or shapes, that could be used to fence a plot of land, which contains the maximum area, using exactly 1000 metres. To start I will be investigating the rectangle family as shown below: From these results, the maximum area using exactly 1000 metres of fencing is the rectangle that measures 250 by 250. Its area is 62500m², which is the biggest area and it is square in shape, which proves that the square is the best to use, when investigating four sided shapes. I have plotted a graph from these results obtained: My next investigation will be using triangles to find the maximum area of land that could be fenced, using exactly 1000 metres. I will be using triangles as shown below: Base/m Sides/m Perpendicular Height/m Area/m² 50 475 474.3 11857.5 100 450 447.2 22360 150 425 418.3 31372.5 200 400 387.3 38730 250 375 353.6 44200 300 350 316.2 47430 350 325 273.9 47932.5 400 300 223.6 44720 450 275 158.1 35572.5 From these results, the maximum area using exactly 1000 metres of fencing is the...

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