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

Fencing Problem - Maths Coursework

Extracts from this document...

Introduction

Fencing Problem – Math’s Coursework

A farmer has exactly 1000 meters of fencing and wants to fence of a plot of level land. She is not concerned about the shape of the plot but it must have a perimeter of 1000 m. She wishes to fence of a plot of land that contains the maximum area. I am going to investigate which shape is best for this and why.

I am going to start by investigating the different rectangles; all that have a perimeter of 1000 meters.

...read more.

Middle

80

33600

430

70

30100

440

60

26400

450

50

22500

460

40

18400

470

30

14100

480

20

9600

490

10

4900

Using this table I can draw a graph of height against area. This is on the next sheet.

As you can see, the graph has formed a parabola. According to the table and the graph, the rectangle with a base of 250m has the greatest area. This shape is also called a square.

Now that I have found that a square has the greatest area of the rectangles group, I am going to find the triangle with the largest area. I am only going to use isosceles triangles because if I know the base I can work out the other 2 lengths because they are the same. If the base is 200m long then I can subtract that from 1000 and divide it by two. This means that I can say that:

Side = (1000 – 200) / 2 = 400

To work out the area I need to know the height of the triangle. Tow ork out the height I can use Pythagoras’ Theorem.

...read more.

Conclusion

As you can see from the graph, the line straightens out as the number of side’s increases. Because I am increasing the sides by large amounts and they are not changing I am going to see what the result is for a circle. Circles have an infinite number of sides, so I cannot find the area using the equation for the other shapes. I can find out the area by using π. To work out the circumference of the cir le the equation is πd. I can rearrange this so that diameter equals circumference/π. From that I can work out the area using the πr² equation.

DIAMETER = 1000 / π = 318.310

RADIUS = 318.310 / 2 = 159.155

AREA = π × 159.155² = 79577.472m²

From this I have concluded that a circle has the largest area when using a similar circumference. This means that the farmer should use a circle for her plot of land so that she can gain the maximum 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. GCSE Maths Coursework Growing Shapes

    20 D1 As there are all 4's in the D1 column, the formula contains 4n. Pattern no. (n) No. of outer vertices No. of outer vertices - 4n 1 4 0 2 8 0 3 12 0 4 16 0 5 20 0 Formula for number of outer vertices =

  2. Fencing Problem

    Pentagon I am now going to try and figure out the area of a pentagon. I hypothesize that the area of the Pentagon will be larger than the area of a Square as it has 5 equal sides. Also I have noticed that the more equal sides a shape has the larger the area is.

  1. Fencing problem.

    I shall now substitute the height into the formula below: Area of a triangle = 1/2 � Base � Height Area of a triangle = 1/2 � 142.9 � 148.6 = 10617.5m2 I have now found the area of one triangle.

  2. Maths Coursework - The Fencing Problem

    400 100 40000 410 90 36900 420 80 33600 430 70 30100 440 60 26400 450 50 22500 460 40 18400 470 30 14100 480 20 9600 490 10 4900 The Parallelogram I knew that the side length that produces the largest area would be 250 by 250.

  1. The Fencing Problem

    We can clearly see that the only area that an equilateral triangle will produce is 48112.63m�; this is the maximum area any triangle can hold while observing the 1000m perimeter.

  2. The Fencing Problem

    Therefore the other angles = (180-51.4)/2=64.3? each. I can split the isosceles triangle into 2 equal right-angled triangles and work out the area of the triangle, using trigonometry. I also know that each side of the heptagon is 1000/7=142.9m. I will use tangent to work out the height of the triangle because I know the adjacent (71.45m)

  1. t shape t toal

    25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 Here we can see a translation of +4 vertically and +4 horizontally. The original T-shape has a T-total of 171, and the translated T-shape has a T-total of 51.

  2. Math Coursework Fencing

    Thus, if a and b are the two parallel sides and h is the distance (height) between the parallels, the area formula is as follows: I started by drawing an isosceles trapezium and finding out its area a c d Because it is an isosceles trapezium c and d will be equal.

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