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Area and perimeter_10_r5
- 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. Perimeter 25/02/2013 Learning 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. Perimeter • Perimeter: Thedistance around the outside of a shape • To calculate the perimeter, you add together all the sides of a shape
- 4. Perimeter 10cm • Example: 3cm P = 10 + 3 + 10 + 3 P = 26cm
- 5. Perimeter • Calculate theperimeter 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. Perimeter • Compound shape:a 2D shape made up of many shapes
- 7. Perimeter 10m Can I calculate the perimeter of this shape? 15m I need to find the 21m length of the 25m 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. Perimeter • Example: 10cm Perimeter = 5 + 5cm as it is a 5cm rectangle 10 + 5 + 3 + 9 + 4 +9+3 3cm 3cm Perimeter = 48cm 9cm 9cm 10 – 3 – 3 = 4cm
- 9. Starter • Calculate theperimeter of the following shapes 5cm 4m 18m 11cm 5m 20m
- 10. Perimeter 25/02/2013 Learning 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. Your turn… • Exercise5A, page 97
- 12. Area • How canI calculate the area of this rectangle? • Count the squares inside the shape • Multiply the width by the length
- 13. Area of arectangle • Area of a rectangle = length x width Area = 4 x 12 4cm Area = 48cm2 12cm
- 14. Starter • How manyrectangles can you design that have an area of 24cm2? • Do the sides have to be whole numbers?
- 15. Area of Triangles 25/02/2013 Learning 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. Area of Triangles Height Base • Area of a triangle = ½ x base x height = ½bh
- 17. Area of aTriangle • Calculate the area of this triangle. 4cm 12cm Area = ½ x 4 x 12 = 24cm2
- 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. Your turn… • Page104, Exercise 5E, Qs 1 to 4.
- 20. Starter • Complete theworksheet in your workbook – Show all your working out – Remember to use the correct units!
- 21. Grade D Area of Triangles 25/02/2013 Learning 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. Area of Triangles •Perpendicular – “at right angles to”
- 23. Area of Triangles The perpendicular height • Area = base x height 2 base height height height base base
- 24. Area of Triangles •Find the area of the following triangle. 7cm 4cm 6cm 10cm Area = ½ x 10 x 6 = 30cm2
- 25. Area of Triangles 12cm 15m 8m 9cm 18m 11cm 15cm 5m
- 26. Grade D Area of Triangles 25/02/2013 Learning 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. Area of Triangles 1 2 20m 20m 17cm 12cm 10m 36cm2 125m2 6cm 25m 3 27km 5km 3km 45km2 30km
- 28. Some work… • Inyour workbooks, work through pages 65 and 66.
- 29. Home Learning • Completethe worksheet in your books • Show all working out • DUE: Monday 19th September
- 30. Starter • Match theshape 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. Parallelograms and Trapezia GradeD 25/02/2013 Learning Objectives • Able to calculate the area of triangles • Able to calculate the area of parallelograms and trapezia
- 32. Area of aParallelogram Area of Parallelogram = base x perpendicular height height Base Area = 6 x 12 9cm 6cm = 72cm2 12cm
- 33. Area of aTrapezium a h b Area of Trapezium = ½ (a + b) x h a and b are the parallel sides
- 34. Starter • Calculate thearea of these trapezia. 15cm 8cm 12cm 8cm 7cm 14cm
- 35. Area of CompoundShapes Grade D 25/02/2013 Learning Objectives: • Able to calculate areas of trapezia • Able to split up a compound shape • Able to find the area of a compound shape
- 36. Compound Shapes • Tofind the area of compound shapes, split them up into their composite shapes. • Find the area of each shape, then add them together
- 37. Compound Shapes 8cm Area A = 8 x 5 A 5cm = 40cm2 Area B = 11 x 2 = 22cm2 B 11cm Total Area = 40 + 22 = 62cm2 2cm
- 38. Compound Shapes 8cm 7cm 1cm 15cm
- 39. Your turn… • Completethe worksheet in your work books.
- 40. Starter • The rectanglesbelow have the same area. Find the value of x. 5cm 20cm 8cm
- 41. Grade D/C Circles 25/02/2013 Learning 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. 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. Circles Diameter = 2 x radius Radius = diameter ÷ 2 6cm 12cm 6cm
- 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. Circles 1) Measure thecircumference and diameter of the objects and record them in the table. 2) Divide the circumference by the diameter. Write your results in the table 3) Can you spot the common link?
- 46. Object Circumference Diameter C÷d
- 47. Starter Calculate thearea of each of the following shapes. 13cm 6cm 7cm 5cm 7cm 12cm 11cm 4cm 15cm 6cm 18cm
- 48. Grade D/C Circles 25/02/2013 Learning 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. Circles • This relationshipbetween 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. Circles • Circumference =∏ x diameter OR • Circumference = 2 x ∏ x radius
- 51. Circles Circumference = 2∏r C=2x∏x4 4cm C=8x∏ C = 25.13cm (2dp)
- 52. Circles Find the circumference of the circle. 7cm C=2x∏x7 C = 14 x ∏ C = 43.98cm (2dp)
- 53. Starter • Calculate thearea of • Calculate the this trapezium circumference of this 4cm circle 11cm 6cm 8cm 10cm
- 54. Grade D/C Circumference 25/02/2013 Learning 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. Circles If I wantto find the circumference of these circles, which formula should 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. Circles • Page – Exercise – Questions
- 57. Starter • On yourwhiteboard, calculate the circumference of the following shapes. 10cm 9cm
- 58. Grade C Area of Circles 25/02/2013 Learning 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. Area of Circles •Area = ∏ x radius2 • Area = ∏r2 radius
- 60. Area of Circles •Area = ∏r2 • Area = ∏ x 42 • Area = ∏ x 4 x 4 4cm • Area = 16 x ∏ • Area = 50.27cm2
- 61. Areas of Circles 7cm
- 62. Area of Circles •Radius = 18 ÷ 2 = 9cm • Area = ∏ x 92 18cm • Area = 81 x ∏ • Area = 254.47cm2
- 63.
- 64. Your turn… • Page364 – 366 – Exercise 16C – Questions 1, 3, 5, 6, 7*, 9*