GCSE Maths Coursework

And 4X4 is also how to work out the area therefore they both come to make 16

This all because a square has EQUAL SIDES

My interpretation does not work with rectangles because the sides are NOT EQUAL

2.Triangle

Working out the equation for the area of an equilateral triangle

1cm 1cm

1cm

An equilateral triangle is one were all the sides have equal length ie. All 1cm

Area = 1/2 X L X L x sin60

Size of sides of triangle, cm

Perimeter, cm

Area, cm squared

3

0.43

2

6

.73

3

9

3.89

4

2

6.92

5

5

0.82

6

8

5.5

7

21

21.21

8

24

27.71

Interpretation

This table shows me that the length of the sides of the equable triangle is between 7 and 6 because the perimeter for 6 is > its area and for 7 the perimeter < its area. There can only be one equable shape for equalaterial triangles because of the required equal sides making increasing a side and not increasing the other sides impossible

Equable Rectangles

L

W W

L

Area of rectangle = L x W

Perimeter = L + L + W + W

Since a=p

L x W = 2L + 2W = EQUABLE SHAPE

L (W - 2) = 2W

Therefore...

L = (2 X W) DIVIDED BY (W - 2)

Width

Length

Perim/area

-2

2

0

3

6

8

4

4

6

5

3.3 recurring

6.5

6

3

2

7

2.5

* 1 and 2 can not be equable shapes because you can not have a length of -2 or 0. It must be at least 1.

* With rectangles there is an infinite number of equable shapes, it occurs for every size over 2 as my table proves.

* The graph for this would be a gentle curve downwards from the value for 3, because this is where it starts properly

The first two values don't count because they are not possible rectangles.

Conclusion

I conclude that with different shapes there is different ways of finding the equable shape(s) and with each different answers and reasons arise, and there is similarities and differences between these. For example, unlike the other two shapes I studied, rectangles have an infinite number of equable shapes, this is due the non equal sides of the shape. With squares there can only be one equable shape because when there is only one way to increase a side length, and that is by increasing them all, and it is also the same with triangles.