Area and perimeter_10_r5

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Area and perimeter_10_r5

  1. 1. Starter• On whiteboards, write down as many units of LENGTH as you can• Write down as many units for AREA as you can EXTENSION: What is the perimeter of this rectangle?
  2. 2. Perimeter 25/02/2013Learning Objectives: Know the key words for perimeter and the units used Able to calculate the perimeter of a rectangle Able to calculate the perimeter of a compound shape
  3. 3. Perimeter• Perimeter: The distance around the outside of a shape• To calculate the perimeter, you add together all the sides of a shape
  4. 4. Perimeter 10cm• Example: 3cm P = 10 + 3 + 10 + 3 P = 26cm
  5. 5. Perimeter• Calculate the perimeter of the following 1cm rectangles: 12cm EXTENSION: 9cm b) Can you a) 4cm calculate the area of these rectangles? 5m c) d) 5cm 5cm 6m
  6. 6. Perimeter• Compound shape: a 2D shape made up of many shapes
  7. 7. Perimeter 10m Can I calculate the perimeter of this shape? 15m I need to find the 21m length of the25m missing sides first. P = 10 + 15 + 21 + 10 + 31 + 25 10m Now I can calculate P = 112m the perimeter by adding up the all the 31m sides.
  8. 8. Perimeter• Example: 10cm Perimeter = 5 + 5cm as it is a5cm rectangle 10 + 5 + 3 + 9 + 4 +9+3 3cm 3cm Perimeter = 48cm 9cm 9cm 10 – 3 – 3 = 4cm
  9. 9. Starter• Calculate the perimeter of the following shapes 5cm 4m 18m11cm 5m 20m
  10. 10. Perimeter 25/02/2013Learning Objectives: Able to calculate the perimeter of a rectangle Able to calculate the perimeter of a compound shape Able to calculate the area of a rectangle
  11. 11. Your turn…• Exercise 5A, page 97
  12. 12. Area• How can I calculate the area of this rectangle? • Count the squares inside the shape • Multiply the width by the length
  13. 13. Area of a rectangle • Area of a rectangle = length x width Area = 4 x 124cm Area = 48cm2 12cm
  14. 14. Starter• How many rectangles can you design that have an area of 24cm2?• Do the sides have to be whole numbers?
  15. 15. Area of Triangles 25/02/2013Learning Objectives:• Able to calculate the area of a rectangle• Able to calculate the area of a triangle• Able to calculate the area of a compound shape
  16. 16. Area of Triangles Height Base• Area of a triangle = ½ x base x height = ½bh
  17. 17. Area of a Triangle• Calculate the area of this triangle. 4cm 12cm Area = ½ x 4 x 12 = 24cm2
  18. 18. Area of Triangles• Find the area of the shaded triangle BCD. 5cm 4cm A B C 6cm Area of ACD = ½ x 9 x 6 = 27cm2 11cm Area of ABD = ½ x 5 x 6 D = 15cm2 Area of BCD = 27 – 15 = 12cm2
  19. 19. Your turn…• Page 104, Exercise 5E, Qs 1 to 4.
  20. 20. Starter• Complete the worksheet in your workbook – Show all your working out – Remember to use the correct units!
  21. 21. Grade D Area of Triangles 25/02/2013Learning Objectives:• Able to calculate the area of a right angled triangle• Able to identify the perpendicular height of a triangle• Able to calculate the area of any triangle
  22. 22. Area of Triangles• Perpendicular – “at right angles to”
  23. 23. Area of Triangles The perpendicular height • Area = base x height 2 base height heightheight base base
  24. 24. Area of Triangles• Find the area of the following triangle. 7cm 4cm 6cm 10cm Area = ½ x 10 x 6 = 30cm2
  25. 25. Area of Triangles 12cm 15m 8m 9cm 18m11cm 15cm 5m
  26. 26. Grade D Area of Triangles 25/02/2013Learning Objectives:• Able to calculate the area of a right-angled triangle• Able to calculate the area of other triangles• Able to calculate the area of a parallelogram
  27. 27. Area of Triangles1 2 20m 20m 17cm 12cm 10m 36cm2 125m2 6cm 25m 3 27km 5km 3km 45km2 30km
  28. 28. Some work…• In your workbooks, work through pages 65 and 66.
  29. 29. Home Learning• Complete the worksheet in your books• Show all working out• DUE: Monday 19th September
  30. 30. Starter• Match the shape to the correct area and perimeter.• There is one perimeter and one area that don’t have a shape. Draw the shape to match the perimeter and area on the blank card.
  31. 31. Parallelograms and TrapeziaGrade D 25/02/2013Learning Objectives• Able to calculate the area of triangles• Able to calculate the area of parallelograms and trapezia
  32. 32. Area of a Parallelogram Area of Parallelogram = base x perpendicular height height Base Area = 6 x 129cm 6cm = 72cm2 12cm
  33. 33. Area of a Trapezium a h bArea of Trapezium = ½ (a + b) x h a and b are the parallel sides
  34. 34. Starter• Calculate the area of these trapezia. 15cm 8cm 12cm 8cm 7cm 14cm
  35. 35. Area of Compound ShapesGrade D 25/02/2013Learning Objectives:• Able to calculate areas of trapezia• Able to split up a compound shape• Able to find the area of a compound shape
  36. 36. Compound Shapes• To find the area of compound shapes, split them up into their composite shapes.• Find the area of each shape, then add them together
  37. 37. Compound Shapes 8cm Area A = 8 x 5 A 5cm = 40cm2 Area B = 11 x 2 = 22cm2B 11cm Total Area = 40 + 22 = 62cm22cm
  38. 38. Compound Shapes 8cm 7cm 1cm15cm
  39. 39. Your turn…• Complete the worksheet in your work books.
  40. 40. Starter• The rectangles below have the same area. Find the value of x. 5cm 20cm 8cm
  41. 41. Grade D/C Circles 25/02/2013Learning Objectives:• Able to calculate the radius and diameter of a circle• Able to use a calculator to find the circumference of a circle• Able to calculate the area of a circle
  42. 42. Circles • Radius – distance from centre to outside of a circle • Diameter – distance from one side of the circle to the other, passing through the centre
  43. 43. Circles Diameter = 2 x radius Radius = diameter ÷ 26cm 12cm 6cm
  44. 44. Circles• Circumference – the distance around the outside of a circle.• You are going to investigate the relationship between the circumference and the diameter.
  45. 45. Circles1) Measure the circumference and diameter of the objects and record them in the table.2) Divide the circumference by the diameter. Write your results in the table3) Can you spot the common link?
  46. 46. Object Circumference Diameter C÷d
  47. 47. Starter Calculate the area of each of the following shapes. 13cm6cm 7cm 5cm 7cm 12cm 11cm 4cm 15cm 6cm 18cm
  48. 48. Grade D/C Circles 25/02/2013Learning Objectives:• Able to calculate the radius and diameter of a circle• Able to use a calculator to find the circumference of a circle• Able to calculate the area of a circle
  49. 49. Circles• This relationship between the circumference and diameter is called ‘pi’• The symbol for pi is ∏• ∏ = 3.1415926….• We often use 3.14 as an approximation• It is found on calculators
  50. 50. Circles• Circumference = ∏ x diameter OR• Circumference = 2 x ∏ x radius
  51. 51. Circles Circumference = 2∏r C=2x∏x44cm C=8x∏ C = 25.13cm (2dp)
  52. 52. Circles Find the circumference of the circle.7cm C=2x∏x7 C = 14 x ∏ C = 43.98cm (2dp)
  53. 53. Starter• Calculate the area of • Calculate the this trapezium circumference of this 4cm circle11cm 6cm 8cm 10cm
  54. 54. Grade D/C Circumference 25/02/2013Learning Objectives:• Able to calculate the radius and diameter of a circle• Able to use a calculator to find the circumference of a circle• Able to calculate the area of a circle
  55. 55. CirclesIf I want to find the circumference of these circles, which formulashould I use? 6cm C=2x∏xr C=∏xd C=2x∏x6 C = ∏ x 14 C = 12 x ∏ C = 43.98 (2dp) C = 37.7cm (1dp)
  56. 56. Circles• Page – Exercise – Questions
  57. 57. Starter• On your whiteboard, calculate the circumference of the following shapes. 10cm 9cm
  58. 58. Grade C Area of Circles 25/02/2013Learning Objectives:• Able to calculate the circumference of a circle• Able to calculate the area of a circle given the radius• Able to calculate the area of a circle given the diameter
  59. 59. Area of Circles• Area = ∏ x radius2• Area = ∏r2 radius
  60. 60. Area of Circles• Area = ∏r2• Area = ∏ x 42• Area = ∏ x 4 x 4 4cm• Area = 16 x ∏• Area = 50.27cm2
  61. 61. Areas of Circles 7cm
  62. 62. Area of Circles• Radius = 18 ÷ 2 = 9cm• Area = ∏ x 92 18cm• Area = 81 x ∏• Area = 254.47cm2
  63. 63. Area of Circles
  64. 64. Your turn…• Page 364 – 366 – Exercise 16C – Questions 1, 3, 5, 6, 7*, 9*

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