• 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...


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.

























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.


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. 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.

  2. Fencing problem.

    found by dividing 3600 by the number of sides of the shape that has been shown above: Exterior angles = 3600 � Number of sides Exterior angles = 3600 � 6 Exterior angles = 600 I shall now find the interior angles of the above shape.

  1. The Fencing Problem

    1000 6945.93 The highest area in this table consists of a parallelogram with a base of 100, sloping height of 400, and interior angle of 90�. With this information I can deduce that the parallelogram with the largest area in the table is in the form of a rectangle.

  2. Fencing Problem

    of the rectangle I am going to figure out the area of the rectangle. I have the height of the rectangle already as the height of the triangle is the also the height for the rectangle. * To find the lengths of the 2 sides of my rectangle I will

  1. t shape t toal

    The original formula is no good. To double check that we have to use a different formula we can try it on a different grid size. 5 by 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

  2. Math Coursework Fencing

    50m a 250m 250m c 450m To find height To find 2x If a < b, do b-a If a > b, do a-b 2x=b-a 2x=450-50 x x h 250 200 Apply Pythagoras theorem to find height Apply trapezium formulae to find area: It is clear that a table I

  1. Geography Investigation: Residential Areas

    Over the course of my investigation I have found that my results often relate back to one of the theories. Each of my conclusions at the end of studying a hypothesis I have commented on whether my results prove or disprove my initial key question.

  2. GCSE Maths Coursework Growing Shapes

    I notice that with pattern 4 in columns when n = 4: 2 lots of (1 + 3 + 5) = 2 x 9 1 lot of 7 = 1 x 7 2 x 9 = 2(n-1)2 7 = 2n - 1 Ts = 2(n-1)2 + 2n - 1 Number of Lines Pattern no.

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