# Mathematics Coursework - Fencing problem

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Introduction

Mathematics Coursework - Fencing Introduction: A framer has a farm that he needs to fence, and I need to investigate and look for the largest area of a plot with the perimeter of 1000 meter. I will start from triangle the least sided shape. (All diagram not drawn to scale) Triangles: Equilateral Triangle: A triangle that has the same length on every side is known as an equilateral triangle. Formula: (Base x Height) ?2 Equilateral Triangle 1: Height: H2+ 166.72 = 333.32 (Pythagoras Theorem) H2 = 111088.89 - 27788.89 H2 = 83300 H = 288.6m (1 d.p.) Area of triangle: (288.62 x 166.7) m = 48112.5m2 (1 d.p.) Isosceles Triangles: Isosceles triangle means a triangle that has two same lengths on the side and the bottom two angles will be the same. Formula: (Base x Height) ?2 Isosceles Triangle 1: Sides 262.5 Base 475 Perimeter: (2 x 262.5 + 475) m = 1000m Height: H2 + 237.52 = 262.52 H2 = 68906.25 - 56406.25 H2 = 12500 H = 111.8m (1 d.p.) Area of triangle: (111.8 x 237.5) m = 26553.3m (1 d.p.) Isosceles Triangle 2: Sides 317 Base 366 Perimeter: (2 x 317 + 366) m = 1000m Height: H2 + 1832 = 3172 H2 = 100489 - 33489 H2 = 67000 H = 258.84m (2 d.p.) Area of triangle: (258.84 x 183) m = 47368.38 m2 (2 d.p.) Right angle triangles: A triangle that has a right angle is called a right angle triangle. ...read more.

Middle

Formula: Base x Height Rectangle 1: Area: (381.5 x 118.5) m = 45207.75m2 Rectangle 2: Area: (206.23 x 293.77) m = 60584.1871m2 Trapeziums: A shape that has two parallel sides, but different length. Formula: (a +b) x h ? 2 Trapezium 1: Perimeter: (3.5 + 4 + 9 + 3.5) m = 20m Ratio: 20=1000 9=X 3.5=Y 4=Z 1000 ? 2 = 50 Length: 9=X 9 x 50 = 450m 3.5=Y 3.5 x 50 = 175m 4=Z 4 x 50 = 200m Height: 752 + H2 = 1752 5625 + H2 = 30625 H2 = 30625 - 5625 H2 = 25000 H = 158 m (3 s.g.) Area: (200 + 450) x 158 ? 2 = 650 x 158 ? 2 = 102700 ? 2 = 51350 m2 Trapezium 2: Perimeter: (15 + 7 + 9 + 7) m = 38 m Ratio: 38=1000 15=X 7=Y 9=Y 1000 ? 38 = 26.32 (2 d.p.) Length: 15=X 15 x 26.32 = 395m (3 s.g.) 7=Y 7 x 26.32 = 184 m (3 s.g.) 9 = Z 9 x 26.32 = 237m (3 s.g.) Height: 792 + H2 = 1842 6241 + H2 = 33856 H2 = 33856 - 6241 H2 = 27615 H = 166.2 m (1 d.p.) Area: (395 + 237) x 166.2 ? 2 = 632 x 166.2 ? 2 = 105038.4 ? 2 = 52519.2 m2 Trapezium 3: Perimeter: (8 + 7 +4 + 7) m = 26m Ratio: 26=1000 8=X 7=Y 4=Z 1000 ? ...read more.

Conclusion

54 0.942477796 1.37638192 137.638192 13763.8192 68819.09602 6 166.6666667 60 60 1.047197551 1.732050808 144.3375673 12028.13061 72168.78365 7 142.8571429 51.42857143 64.28571429 1.121997376 2.076521397 148.3229569 10594.49692 74161.47845 8 125 45 67.5 1.178097245 2.414213562 150.8883476 9430.521728 75444.17382 9 111.1111111 40 70 1.221730476 2.747477419 152.6376344 8479.868579 76318.81721 10 100 36 72 1.256637061 3.077683537 153.8841769 7694.208843 76942.08843 11 90.90909091 32.72727273 73.63636364 1.285196995 3.405687239 154.8039654 7036.543882 77401.9827 12 83.33333333 30 75 1.308996939 3.732050808 155.502117 6479.254874 77751.05849 13 76.92307692 27.69230769 76.15384615 1.329135353 4.057159486 156.0445956 6001.715215 78022.2978 14 71.42857143 25.71428571 77.14285714 1.346396852 4.381286268 156.4745096 5588.375341 78237.25478 15 66.66666667 24 78 1.361356817 4.704630109 156.8210036 5227.366788 78410.50182 16 62.5 22.5 78.75 1.374446786 5.027339492 157.1043591 4909.511223 78552.17956 17 58.82352941 21.17647059 79.41176471 1.385996759 5.349527506 157.3390443 4627.618949 78669.52214 18 55.55555556 20 80 1.396263402 5.67128182 157.5356061 4375.989058 78767.80305 19 52.63157895 18.94736842 80.52631579 1.405449345 5.992671459 157.7018805 4150.049487 78850.94024 20 50 18 81 1.413716694 6.313751515 157.8437879 3946.094697 78921.89393 25 40 14.4 82.8 1.445132621 7.915815088 158.3163018 3166.326035 79158.15088 50 20 7.2 86.4 1.507964474 15.89454484 158.9454484 1589.454484 79472.72422 75 13.33333333 4.8 87.6 1.528908425 23.8592772 159.061848 1060.41232 79530.92399 100 10 3.6 88.2 1.5393804 31.82051595 159.1025798 795.5128988 79551.28988 500 2 0.72 89.64 1.564513141 159.1528487 159.1528487 159.1528487 79576.42435 1000 1 0.36 89.82 1.567654734 318.308839 159.1544195 79.57720975 79577.20975 5000 0.2 0.072 89.964 1.570168008 1591.549221 159.1549221 15.91549221 79577.46107 10000 0.1 0.036 89.982 1.570482168 3183.098757 159.1549379 7.957746893 79577.46893 50000 0.02 0.0072 89.9964 1.570733495 15915.49429 159.1549429 1.591549429 79577.47144 100000 0.01 0.0036 89.9982 1.570764911 31830.98861 159.154943 0.795774715 79577.47152 500000 0.002 0.00072 89.99964 1.570790044 159154.9431 159.1549431 0.159154943 79577.47154 1000000 0.001 0.00036 89.99982 1.570793185 318309.8862 159.1549431 0.079577472 79577.47154 5000000 0.0002 0.000072 89.999964 1.570795698 1591549.431 159.1549431 0.015915494 79577.47156 Spread Sheet ...read more.

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