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Perimeter, Area and Volume

Perimeter, Area and Volume

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Perimeter, Area and Volume

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  1. Perimeter, Area and Volume Grades F to A

  2. Rectangles and Triangles Hyperlinks! Counting Squares Parallelograms and Trapeziums Area – working backwards Circles Compound Shapes Volume of cuboids Volume of prisms Surface area Sectors of circles Volume and surface area of complex shapes

  3. Success Criteria: Where Are We Now?

  4. Area and perimeter by counting and measuring How do I find the area and perimeter of a shape? Grade F

  5. Success Criteria: Where Are We Now?

  6. What are perimeter and area? Perimeter is the length around the outside of a shape. Area is the space inside a shape.

  7. Example The rectangle has a perimeter of: 5 + 3 + 5 + 3 = 16cm The rectangle has a area of: 5 + 5 + 5 = 15cm² Take note of the units! 5 × 3 = 15cm²

  8. Find the perimeter and area of this rectangle: Perimeter = Area = 20cm 24cm²

  9. Success Criteria: Where Are We Now?

  10. Rectangles and Triangles Can I calculate the perimeter and area of a rectangle and triangle? Grade E

  11. Success Criteria: Where Are We Now?

  12. The formulae to remember:

  13. Two examples: Example 1 Example 2 Find the area of this triangle: Area = 5 × 12 ÷ 2 Area = 60cm² ÷ 2 Area = 30cm² Find the area and perimeter of this rectangle: Area = 8 × 6 Area = 48cm² Perimeter = 8 + 6 + 8 + 6 Perimeter = 28cm 13cm 6cm 5cm 8cm 12cm

  14. Have a go at some: Question 1 Question 2 Find the perimeter and area of this rectangle: Find the area of this triangle: 11cm 8cm 7cm 10cm Answer: Area = 88cm² Perimeter = 38cm Answer: 35cm²

  15. Success Criteria: Where Are We Now?

  16. Parallelograms and Trapeziums Can I calculate the area of a parallelogram and trapezium? Grade D

  17. Success Criteria: Where Are We Now?

  18. The formulae:

  19. Two examples Example 1 Example 2 Find the area of this parallelogram: Area = 7 × 5 Area = 35cm² 4cm 5cm 6cm 5cm 7cm 8cm

  20. Have a go at a couple of questions: Question 1 Question 2 Find the area of this trapezium: Find the area of this parallelogram: 12cm 9cm 8cm 10cm 7cm 11cm Answer: 96cm² Answer: 70cm²

  21. Success Criteria: Where Are We Now?

  22. Circles Can I find the circumference and area of a circle? Grade C

  23. Success Criteria: Where Are We Now?

  24. Names to do with circles you must remember: Circumference Radius Diameter Chord Tangent

  25. Formulae you need to remember:

  26. A couple of examples Example 1 Example 2 Find the circumference and area of a circle with a radius of 8cm to 1 dp. Circumference = π × 16 Circumference = 50.3cm Area = π× 8² Area = 201.1cm² Find the circumference and area of a circle with a diameter of 10cm to 1 dp. Circumference = π × 10 Circumference = 31.4cm Area = π× 5² Area = 78.5cm²

  27. Some for you to try: Question 1 Question 2 Find the circumference and area of a circular pond with a diameter of 3m to 1 dp. Find the circumference and area of this circle to 1 dp. 14cm Circumference = 88.0cm Area = 615.8cm² Circumference = 9.4m Area = 7.1m²

  28. Success Criteria: Where Are We Now?

  29. Area – Working Backwards Now you can find the area of shapes, can you find a length having been given the area?

  30. Formulae Reminder:

  31. Find the missing lengths: None of these are drawn to scale ?cm 7cm 6cm Area = 48cm² Area = 21cm² 8cm ?cm 6cm 5cm 8cm ?cm Area = 113.1cm² Area = 32cm² Area = 28cm² 9cm Height = ? 4cm Height = 4cm 12cm Diameter = ?

  32. Success Criteria: Where Are We Now?

  33. Compound Shapes Can I calculate the perimeter and area of a compound shape? Grade C

  34. Success Criteria: Where Are We Now?

  35. What is a compound shape? A compound shape is a shape that is made up of lots of different shapes. The key is to split the complex shape up into simpler shapes, find the areas of the simple shapes then add your areas together.

  36. An example Find the area of this shape: Split it up! Area = 40 + 32 = 72cm² 12cm Area = 8×5 = 40cm² Area = 8×4 = 32cm² 8cm 8cm 3cm

  37. Another example Find the area of this shape: Split it up! Area = 54 + 13.5 = 67.5cm² 3m Area = 9×6 = 54m² 6m 9m

  38. A couple of questions: Question 1 Question 2 Find the area of this shape: Find the area of this shape: 12cm 3cm 5cm 8m 6cm 10m Answer: 66cm² Answer: 119.3m²

  39. Success Criteria: Where Are We Now?

  40. Volume of Cuboids Can I calculate the volume of a cuboid? Grade C

  41. Success Criteria: Where Are We Now?

  42. How to calculate the volume of a cuboid:

  43. An example: Find the volume of this cuboid: Volume = 3 × 5 × 4 Volume = 60cm³ 3cm 4cm 5cm Take note of the units!

  44. Another example, working backwards: Find the height of this cuboid: 280cm³ = 10 × 7 × h h = 280 ÷ (10 × 7) h = 4cm Volume = 280cm³ 7cm 10cm

  45. Two questions to have a go at: Question 1 Question 2 The tank below contains exactly 100 litres of water. How far up the tank does the water go? (Hint: 1 litre = 1000cm³) Find the volume of this cuboid: 8cm 6cm 0.5m 5cm 0.5m 1m Answer: 240cm³ Answer: 0.2m or 20cm

  46. Success Criteria: Where Are We Now?

  47. Prisms Can I calculate the volume of a prism? Grade C

  48. Success Criteria: Where Are We Now?

  49. What is a prism? A prism is a 3D shape that has the same cross-section all the way through. For example: Triangular Prism Hexagonal Prism Cylinder

  50. Calculating the volume of a prism: Find the area of the cross-section then multiply by the length. Volume = Area of cross-section × length