Monday, March 18, 2019
Math Coursework - The Fencing Problem :: Math Coursework Mathematics
The Fencing Problem Introduction A sodbuster has scarce railway yard metres of fencing material and wants to use it to fence a plot of level land. The farmer was not interested in any specific shape of fencing but demanded that the understated two criteria must be met The perimeter body fixed at 1000 metres It must fence the utmost part of land Different shapes of fence with the same perimeter can application different stadiums. The difficulty is finding pop out which shape would cover the maximum area of land use the fencing with a fixed perimeter. orient The aim of the investigation is to find out which shape or shapes of fencing will cover the maximum area of land using considerly 1000 metres of fencing material. Prediction I am predicting that the maximum area of land covered will be achieved by using the fencing shapes with the greatest number of sides. Method I made a itemisation of possible different shapes to be investiga ted and assigned measurements to the sides of the shapes making sure that they operate in within the perimeter of 1000 metres of fencing. I then worked out the areas of each shape using known mathematical formulae and techniques such as Pythagoras theorem to calculate the sides of right angled triangles using trigonometrical functions (sine, tangent and cosine) to calculate either angles or sides of triangles constructed. Sometimes there are no known exact formulae for working out the area of certain shapes such as octagon and much complex polygons. In such cases, given shapes are split into shapes that redeem known formulae for areas and the worked out the areas are added together. Areas of the following shapes were investigated square, rectangle, kite, parallelogram, equilateral triangle, scalene triangle, symmetrical triangle, right-angled triangle, rhombus, pentagon, hexagon, heptagon and octagon. Results The results of the analysis are shown in Table 1 and trope 1. Table 1 showing the areas for the different shapes formed by using the
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