Equable shapes Maths Investigation

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GCSE Maths Coursework: Strand 1 - Making and monitoring decisions

Equable shapes:

The task set is to investigate equable rectangles and further shapes. An equable shape is a shape whose perimeter is 'numerically equal to its area'.

Equable Rectangles

To start off my investigation I decided to experiment by drawing several rectangles with random lengths and widths. My drawings are included on graph paper. (see page )

I then decided using a table I would investigate every rectangle between that had a width or length between one and ten (whole numbers only). I worked out each shapes area and perimeter and if they were equal I highlighted them:

Length

Base

Area

Perimeter

4

2

2

6

3

3

8

4

4

0

5

5

2

6

6

4

7

7

6

8

8

8

9

9

20

0

0

22

2

2

6

2

2

4

8

2

3

6

0

2

4

8

2

2

5

0

4

2

6

2

6

2

7

4

8

2

8

6

20

2

9

8

22

2

0

20

24

3

3

8

3

2

6

0

3

3

9

2

3

4

2

4

3

5

5

6

3

6

8

8

3

7

21

20

3

8

24

22

3

9

27

24

3

0

30

26

4

4

0

4

2

8

2

4

3

2

4

4

4

6

6

4

5

20

8

4

6

24

20

4

7

28

22

4

8

32

24

4

9

36

26

4

0

40

28

5

5

2

5

2

0

4

5

3

5

6

5

4

20

8

5

5

25

20

5

6

30

22

5

7

35

24

5

8

40

26

5

9

45

28

5

0

50

30

6

6

4

6

2

2

6

6

3

8

8

6

4

24

20

6

5

30

22

6

6

36

24

6

7

42

26

6

8

48

28

6

9

54

30

6

0

60

32

7

7

6

7

2

4

8

7

3

21

20

7

4

28

22

7

5

35

24

7

6

42

26

7

7

49

28

7

8

56

30

7

9

63

32

7

0

70

34

8

8

8

8

2

6
Join now!

20

8

3

24

22

8

4

32

24

8

5

40

26

8

6

48

28

8

7

56

30

8

8

64

32

8

9

72

34

8

0

80

36

9

9

20

9

2

8

22

9

3

27

24

9

4

36

26

9

5
...

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