• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
• Level: GCSE
• Subject: Maths
• Word count: 1890

# Fencing Problem

Extracts from this document...

Introduction

GCSE Maths Coursework:- By Sarah Wolfe, 10Ba2 A farmer has exactly 1000 metres of fencing and wants t fence off plot of level land. I am going to come up with a range of shapes which has a perimeter or circumference of 1000 metres. For each shape I draw I will draw different size ones and find their areas. The reason for finding their areas is because the farmer wants to find a shape with the maximum area. To get started on this exercise, I am first of all going to come with a shape which I think is easiest to use; this will be a rectangle. 1) Perimeter = 450 + 50 + 450 + 50 = 1000m Area = 450 x 50 = 22,500m 2) Perimeter = 400 + 100 + 400 + 100 = 1000m Area = 400 x 100 = 40,000m 3) Perimeter = 385 + 115 + 385 +115 = 1000m Area = 385 x 115 = 44,275m 4) Perimeter = 375 + 125 + 375+ 125 = 1000m Area = 375 x 125 = 46,875m 5) Perimeter = 350 + 150 +350 +150 = 1000m Area = 350 x 150 = 52,500m 6) Perimeter = 325 +175+325 +175 = 1000m Area = 325 x 175 =56,875m Whilst finding the areas of these shapes, I'm finding that when I decrease the size of the length and increase the width, the area seems to get bigger. ...read more.

Middle

I predict that, like the square, the equilateral triangle will give the biggest area. 333.3 = 166.6 + h 111,111.1 = 277,7.7+ h h = 111,111.1- 277,7.7 h = 108,333.4 h = 108,333.4 h = 329.1m Area = b x h 2 = 333.3 x 329.1 2 Area = 54,850 m (to 1d.p) I am going to do another table, so I can see clearly the areas I have already found. Base (m) Height (m) Area (m ) 100 450 22,350 200 400 38,700 300 350 47,400 350 325 47,950 33.3 33.3 54,850 400 300 44,800 My predication was right and the reason I know this is because when you increase the length higher 33.3m, then the area starts to decrease, as you can see in my table. I am not going to do a graph, as I know it will give me the same sort of graph when I did one for the square; the graph will be symmetrical. I think that this will be the pattern for all of the shapes I do; the one which is equilateral will give the biggest area of that family. It seems to me that the shapes with the smaller sides, give the smallest area, so I am now going to move on to using shapes with more sides; the first one I will start with will be a pentagon. I am going to stick to finding the area of a regular pentagon because, before when finding the areas of the rectangles and triangles, my conclusion has been that the shape which is equilateral, gives the biggest area. ...read more.

Conclusion

Here are a set of instructions of how I did it. 1) From the centre of 2) Then, find the central the shape, split it up angle. (360 the into equal triangles. number of sides) Then label the length of each side. (1000m the number of sides) 4) Once you have found 3) Now find the area the area of that triangle, of one of the triangles; multiply the area by the to do this, you need to number of sides. This find the height first, now gives the final area using trigonometry. of that shape. I could also use a formula; e.g if I were to find the area of a 20 sided shape. I could use 'n' as the number of sides 1) Split it up into 20 triangles 2) Find central angle - 360 = ? 20 3) Find area of each triangle- need height (trigonometry) 4) 'n' (20) x area of one triangle = total area of shape Now I have got worked out the area of the all possible shapes, I am now going to put the shapes with their biggest area, into a table. Shape Area m (best area of shape) Rectangle (square) 62,500m Triangle 54,850m Pentagon 68,800m Hexagon 72,150m Octagon 75,450m 10 sided shape 20 sided shape Circle 79,572m I am now going to increase the number of sides a lot higher. I am not going to do the ones in between as I know already that the more sides I have, the area will be bigger. I am going to do a few more examples ...read more.

The above preview is unformatted text

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

# Related GCSE Fencing Problem essays

1. ## Investigating different shapes to see which gives the biggest perimeter

The graph shows that the area of an isosceles triangle increases as the length of the base increases; however only up to the base length of a regular triangle with equal sides. At this point, this is the biggest triangle with a perimeter of 1000m and area of 48112.52m�.

2. ## Fencing problem.

2 = AF2 + (150m) 2 50625m2 = AF2 + 2250m2 AF2 = 50625m2 - 2250m2 AF2 = 28125m2 AF2 = V28125m2 AF = 167.71m2 I shall now substitute the height into the formula below: Area of a triangle = 1/2 � Base � Height Area of a triangle =

1. ## The Fencing Problem

and the resulting value is the area. Area = {1/2[(1000 � 10) x h]} x 10 100 100 100 100 100 100 100 100 100 100 h 100 50 Regular Polygons - Pentadecagon (15-sided-shape) As shown, I have divided the polygon into triangles, and found the area of one of the triangles; using trigonometry (tan)

2. ## t shape t toal

and translating it on various grids. Data from 4 by 4 grid Data from 5 by 5 grid Data from 6 by 6 grid I will now look at the data I have collected algebraically. Data from 4 by 4 grid 4 + 8 + 12 + 7 + 6 = 37 T + (T-2)

1. ## t shape t toal

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 The Total amount of numbers inside the T shape is 11+12+13+8+18=62 The 11 at the left of the T-Shape will be called the T-Number.

2. ## t shape t toal

x 7 49 7 x 7 8 x 8 56 8 x 7 9 x 9 63 9 x 7 10 x 10 70 10 x 7 11 x 11 77 11 x 7 This grid shows the relation ship between g and the number you take away.

1. ## Geography Investigation: Residential Areas

higher in the CBD and gets better as you work your way out from the centre. In theory, the newer, planned houses are on the outskirts of the town, thus they will have a lower index of decay. However, the nineteenth century, older, unplanned houses in the more central part of town should have a higher index of decay.

2. ## Maths GCSE Courswork

The next isosceles triangle has two sides of length 320m and a base of 360m. Base of one triangle = 360 /2 = 180m Length A = c2 - b2 = a2 = 3202 - 1802 = 700002 = V70000 = 264.57m Area = base x height / 2 =

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