# Fencing Problem

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Introduction

Fencing Problem Introduction I am going to find out which shape will give the maximum area only using 1000m of fencing. I will also prove that the shape I find is the correct one. Triangles - isosceles To find the area of an isosceles triangle I multiplied the base and the height then divided the answer by 2. I already had the base but not the height so I had to figure out the height using the base and 2 sides. To do this I halved the base and focused on 1 half of the triangle. I then used Pythagoras to figure out the height of the triangle. Once I had the height of my triangle I multiplied it by the base and divided it by 2 to figure out the area. ...read more.

Middle

To find the area we will use spreadsheets to find out all the different areas of each triangle. To figure out the height of each triangle we used the formulae =SQRT((POWER(B2,2))-(POWER(A2/2,2))) To figure out the area of each triangle we used the formulae =(A2*B2)/2 E.g. (449.5�-0.5�=249500) (V249500=499.4997) Squares/Rectangles To find the area of a square I had to multiply 250 x 250 because 1000 � 4 = 250. In theory this should give me the largest area of a polygon with a perimeter of 1000m. To find the area of a rectangle I will use a spreadsheet to try and find the rectangle with the largest area. To work out the area of a rectangle I will use the equation L x W = A We used squares and rectangles because they are 2 of the easiest shapes to calculate and the rectangle also gives a large range of outcomes. ...read more.

Conclusion

To do this we cut the triangle in half to give us 2 right angled triangles then we do the calculation: - 83.33333335 � tan30 = 144.34 (2 d.p) To find the area of one triangle we do the calculation: - 0.5 x 166.6666667 x 144.34(H) = 12028.3 We used hexagons to give us a greater range of answers to find are largest area from. However there is only one possible answer for the regular hexagon. The more sides we investigate in a polygon the smaller the increase in area will be. We no this because the graph shows the increase slowing and the area stop increasing. Also the more sides the more it looks like a circle. This will explain why the area stops increasing because it will reach the same amount of area as a circle. ?? ?? ?? ?? Jon Campling Maths Coursework Mr.McEvoy ...read more.

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