Fencing Problem

In order to find the area of the isosceles triangle we need the height. To do this we half the triangle to give 2 right angled triangles. We then used Pythagoras theorem to find the height of the triangle (a²+b²=c²). 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.

(449.5²-0.5²=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. It does this because we can change both the length and width. The rectangle can start with a length of 1m, 2m, 3m etc.

We suspect the biggest area will be when the length and width are both 250m.

To find the area of a rectangle we need the length and the width. We then multiply the length and width together to find the area. To find all the areas we used a spreadsheet.

To figure out the area of each rectangle we used the formulae

=A2*B2

E.g. (250 x 250 = 62500)

Regular Hexagon

To find the area of a regular hexagon we first divided it into 6 equal triangles were each angle inside the triangles is 60º

(Split into 6 equal triangles)

166.6666667m

To find the area of the triangle we have to find out the height of the triangle. 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