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GCSE Maths Coursework

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Introduction

GCSE Maths Coursework An equable shape is one in which: The perimeter and area is equal Find out what you can do about these shapes Different Shapes 1. Square Size of square Perimeter Area 0 0 0 1 4 1 2 8 4 3 12 9 4 16 16 5 20 25 6 24 36 7 28 49 Perimeter = 4 + 4 + 4 + 4 = 16 Area = 4 X 4 = 16 Interpretation When the size is 4 the perimeter and area are both 16 therefore the equable shape for square has the sides of 4. The reason that with a square with size of 4 is equable because. A square has 4 sides therefore to find the perimeter you times the sides to 4. ...read more.

Middle

All 1cm Area = 1/2 X L X L x sin60 Size of sides of triangle, cm Perimeter, cm Area, cm squared 1 3 0.43 2 6 1.73 3 9 3.89 4 12 6.92 5 15 10.82 6 18 15.5 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) ...read more.

Conclusion

* 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. ...read more.

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