• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

The Fencing Problem

Extracts from this document...

Introduction

GCSE Maths Coursework

The Fencing Problem –

To investigate shapes with a perimeter of 1000m and find the largest area this project will be divided into three main sectors.

The first will be investigating shapes with different number of vertices, Triangles, Squares, and different polygons.

The Second will be introducing algebra to make calculating the areas easier. This may only work for regular shapes, I predict that regular shapes will have biggest areas, I hope to prove this in my investigation.

Finally displaying graphs and tables to verify patterns in areas and possible coherency’s.

...read more.

Middle

74129.37566m2

Octagon (Regular, 8 sides)

image00.png

Triangle is a section of the octagon.

                                                 Octagon = 75444.17382m2

Dodecagon (Regular, 10 sides)

image00.png

Triangle is a section of the dodecagon.

                                       Dodecagon = 76942.08842m2

Circle

Circumference = 1000m

Diameter = 318.3098m

Radius = 159.1549m

Area = Πr2

Area = 3.14 X 159.15492 = 79577.42845m2

Circle = 79577.42845m2

Π

times

r2

=

Area

3.1415926454…

    x

25330.28219

=

79577.42845m2

image01.jpg

So far I have been using basic algebra to calculate the areas of the shapes.

My results so far have proved my prediction that the higher the number of sides, the larger the area, with the circle being the largest.

I feel that I can change my formula so that there is only one variable, the number of vertices.

         (2(250/n)2)

...read more.

Conclusion

d>

Area (m2)

n

(2(500/n)2) X TAN (90-(180/n)) n

3

48112.52243

4

62500

5

68819.09602

6

72168.78365

7

74161.47845

8

75444.17382

9

76318.81721

10

76942.08843

11

77401.9827

12

77751.05849

16

78552.17956

18

78767.80305

20

78921.89393

25

79158.15088

50

79472.72422

100

79551.28988

Circle

79577.42845


This table shows that a hundred sided shape still has a smaller area than a circle.

As there are more vertices in a shape, the difference between the previous one becomes less, so eventually, a million sided shape would not only look very much like a circle, but would also have a very similar area.

 This investigation has proved that the largest areas come from shapes with the most sides, the largest being a circle with an infinite number of sides.

The shape of the fence that the farmer should build would be a circle to get the largest area.

...read more.

This student written piece of work is one of many that can be found in our GCSE Fencing Problem section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Fencing Problem essays

  1. Fencing Problem

    1000 m Instead of drawing and working out the area of each parallelogram on Microsoft Word I have formulated a spreadsheet (with a formula) with the aid of Microsoft Excel to speed up the lengthy process of working out the area of parallelograms.

  2. Fencing problem.

    I shall half the interior angle to find this angle: Angle OED = 1200 � 2 = 600 To find Angle EOD = 180 - (60 + 60) Angle EOD = 600 ? EOG = 60 � 2 = 300 I shall use trigonometry to find the height of the above triangle.

  1. The Fencing Problem

    50 x 450 = 22500 50 400 2) 100 x 400 = 40000 100 350 3) 150 x 350 = 52500 150 300 4) 200 x 300 = 60000 200 250 5) 250 x 250 = 62500 250 After the square, the 6th shape's area would be equivalent to that of the 4th shape.

  2. Geography Investigation: Residential Areas

    Most of my hypotheses will use more than one of my methods and nearly all of hypotheses will be backed up with photographic evidence. Data Presentation and Interpretation 1) The intangible factors will have a higher rating on the outskirts of Basingstoke compared to the inner city areas.

  1. Fencing Problem

    62.5 2.41 x 62.5 = h 150.625 = h 1/2 x 125 x 150.625 = 9414.0625 9414.0625 x 8 = 75312.5 Area = 75312.5m� Nonagons I am now going to look at a Nonagon to find out its area when using 1000meters of fencing.

  2. Maths GCSE Courswork

    Area = base x height / 2 = 380 x 244.95 / 2 = 93081 / 2 = 46540.5m2 OR Heron's Formula: Area = = 500 (500 - 310)(500 - 380)(500 - 310) = 2166000000 = V2166000000 = 46540.5m2 The area of this isosceles triangle is 46540.5m2.

  1. Fencing Problem

    The perimeter of each triangle is 1000 meters, therefore the equation for it is: 2L + B = 1000m (where L= Length of the sides and B= base) We have to remember that an isosceles triangle has two sides equal in size.

  2. The Fencing Problem

    � 2 (223.607 x 400) � 2 89,442.7191 � 2 area = 44721.360m� Therefore the area of the isosceles above (not drawn to scale) has an area of 44721.360m�. Now I must do this for lots of triangles so that I can eventually find the triangle with the largest area.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work