2. Perimeter and Area A look at a few basic shapes

3. Perimeter

4. This little square represents a bigger square, one yard in length, and one yard in width.

5. And this is Stamford Bridge (football!)

6. Stamford Bridge football pitch is 110 yards long 110 yards

7. 75 yards and 75 yards wide

8. 110 yards 75 yards

9. 110 yards 75 yards 110 yards 75 yards What is the perimeter of the football pitch?

10. 110 yards 75 yards 110 yards 75 yards 110 + 75 + 110 + 75 = 370 yards

11. Our classroom is approximately 8 metres by 5 metres What is the perimeter?

12. 8 m 5 m Our classroom

13. 8 m 5 m Our classroom 8 m 5 m 8 + 5 + 8 + 5 = 26 metres

14. Question? How do we find the perimeter of a triangle? Answer: Let Google Maps do the measuring for us.

18. The perimeter of the Bermuda Triangle is approximately 4700 km

19. Or 2922 miles

20. 5 m 4 m 3 m The perimeter of this triangle? 3 + 4 + 5 = 12 metres

21. 13 cm 12 cm 5 cm The perimeter of this triangle? 5 + 12 + 13 = 30 cm

22. These TETROMINOES are all made from four squares Do they all have the same perimeter?

23. I get the following: 10 units 8 units 10 units

24. Pause for Play Draw some shapes with a perimeter of 20 centimetres.

25. Let’s go back to Stamford Bridge What is the perimeter of that circle in the middle? Actually, on a circle it is called the circumference

26. According to BBC Sport, it has a radius of 10 yards. Which is from the centre of the circle to the circumference. 10 yards

27. If the radius is 10 yards, then the diameter is 20 yards. The circumference is about three times the diameter. So the circumference is about 3 x 20 = 60 yards 10 yards 20 yards

28. 60 yards

29. If you have a calculator, then you could say it is 3.1, or 3.14, or 3.142 times the diameter. If you have a posh calculator, you could use the π button. 10 yards 20 yards

30. Pi – the Greek letter π, which represents the ratio of the circumference to the diameter of a circle. We can’t actually write it down exactly. But we can write it to as many decimal places as we want.

31. If you have a computer you could use a thousand decimal places…

32. 3.1415926535897932384626433832795028841971693993751058 209749445923078164062862089986280348253421170679821480 865132823066470938446095505822317253594081284811174502 841027019385211055596446229489549303819644288109756659 33446128475648233786783165271201909145648566923460348 61045432664821339360726024914127372458700660631558817 488152092096282925409171536436789259036001133053054882 046652138414695194151160943305727036575959195309218611 738193261179310511854807446237996274956735188575272489 122793818301194912983367336244065664308602139494639522 47371907021798609437027705392171762931767523846748184 67669405132000568127145263560827785771342757789609173 63717872146844090122495343014654958537105079227968925 892354201995611212902196086403441815981362977477130996 051870721134999999837297804995105973173281609631859502 445945534690830264252230825334468503526193118817101000 31378387528865875332083814206171776691473035982534904 287554687311595628638823537875937519577818577805321712 2680661300192787661119590921642019…

33. Pause for Play 8 cm 6 cm 4 cm Which has the greatest perimeter?

34. Area Return to the classroom

35. 8 m 5 m What do we use to measure area?

36. Square metres (or square yards, or square inches, or square centimetres…)

37. 8 m 5 m How many square metres?

38. 8 m 2

39. 8 m 5 m 5 x 8 = 40 square metres, or 40 m 2

40. Pause for Play Draw some rectangles with an area of 20 square centimetres. Do they have the same perimeter?

41. 110 yards 75 yards What, in square yards, is the area of Stamford Bridge?

42. 110 yards 75 yards 110 x 75 = 8250 square yards

43. What about a triangle - how do we find the area?

44. Start with a simple one: 12 cm 5 cm

45. What if we ‘double up’? 12 cm 5 cm

46. Area of the rectangle? 12 cm 5 cm Area of the triangle?

47. Area of the rectangle = 60 cm 2 12 cm 5 cm Area of the triangle = 30 cm 2

48. Slightly more complicated: 3 cm 8 cm

49. But we can still ‘double up’

50. 8 cm 3 cm

51. Area of rectangle = 3 x 8 = 24 8 cm 3 cm Area of triangle = (3 x 8) ÷ 2 = 12 cm 2

52. And a parallelogram?

53. Make some cuts:

55. And then some swaps:

56. And we are back to a rectangle:

57. The original: 3 cm 7 cm

58. And the new one: 7 cm 3 cm

59. The area = 7 x 3 = 21 cm 2 7 cm 3 cm

60. Pause for Play Experiment with square paper and see if you can find a method of calculating the area of a trapezium.

61. 5 m 2 m4 m3 m 9 m What is the area of this trapezium?

62. 5 m 2 m4 m3 m 9 m One possible method, giving 32.5m 2 : 5 m 2 20 m 2 7.5 m 2

63. 5 m 4 m 9 m Another method

64. c a b And the formula:

65. And finally a circle A bit trickier to explain

66. Chop it up a bit

67. And rearrange the parts Not a lot of use!

68. Chop it into smaller sectors

69. And rearrange the parts again And it is starting to look like something else

70. Even smaller sectors:

71. And rearrange the parts yet again And it’s near enough to a rectangle for me!

72. =

73. What is the length and width?

74. The width is the radius of the original circle r

75. And the length is half the circumference Since the circumference = πd Then half the circumference = πr Because r = ½d

76. So we have approximately a rectangle r πrπr

77. And the area will be π r × r r πrπr So area of a circle = π × r × r = π × r 2

78. And a final return to our little football circle: Area = π × r 2 = 3.14 × 10 2 = 3.14 × 100 = 314 square yards 10 yards

79. Got it? For Circles: Cherry Pie’s Delicious Apple Pies R 2 In other words C = π d A = π r 2

80. Pause for Play 8 cm 6 cm 4 cm Which has the greatest area? Hint: Square paper, isometric paper, and a pair of scissors?

81. And that’s more than enough! Perimeter of shapes made from straight lines Circumference of circles Area of rectangles, triangles, parallelograms and trapeziums Area of circles