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.

) 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.

7) Perimeter = 275 + 225 + 275 +225

= 1000m

Area = 275 x 225

= 61, 875m

8) Perimeter = 265 +235 + 265+ 235

= 1000m

Area = 265 x 235

= 62,275m

9) Perimeter = 250 +250 +250+250

= 1000m

Area = 250 x 250

= 62,500m

To make the process easier and quicker, I am now going to put the areas I have already found into a table.

Table to show areas of rectangles

Length (m)

Width (m)

Area (m )

450

50

22,500

400

00

40,000

385

15

44,275

375

25

46,875

350

50

52,500

325

75

56,875

275

225

61,875

265

235

62,275

250

250

62,500

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.

) 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.

7) Perimeter = 275 + 225 + 275 +225

= 1000m

Area = 275 x 225

= 61, 875m

8) Perimeter = 265 +235 + 265+ 235

= 1000m

Area = 265 x 235

= 62,275m

9) Perimeter = 250 +250 +250+250

= 1000m

Area = 250 x 250

= 62,500m

To make the process easier and quicker, I am now going to put the areas I have already found into a table.

Table to show areas of rectangles

Length (m)

Width (m)

Area (m )

450

50

22,500

400

00

40,000

385

15

44,275

375

25

46,875

350

50

52,500

325

75

56,875

275

225

61,875

265

235

62,275

250

250

62,500