Area And Volume Spaced Learning

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Slideshow designed for a 'Spaced Learning' revision session for GCSE Maths.

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Area And Volume Spaced Learning

  1. 1. Area and Volume Using formulae
  2. 2. Finding Area and Perimeter of a Square or Rectangle <ul><li>Area is the measure of the amount of space a shape covers </li></ul><ul><li>Perimeter is the distance all the way around the outside. </li></ul>Area of a rectangle = length × width A = l × w Perimeter = 2 × (length and width) length width
  3. 3. Finding Area of a Triangle <ul><li>A triangle takes up half the space of a rectangle with the same side lengths. </li></ul>length (base) width (height) Area of a triangle = ½ length × width A = ½ l×w
  4. 4. Length Perpendicular height Area of a parallelogram = length × perpendicular height A = l×h Finding Area of a Parallelogram
  5. 5. Perpendicular height Length a Length b Finding Area of a Trapezium Area of a trapezium = ½ (length a + length b) × perp height A = ½ (a+b) × h
  6. 6. Radius, r Diameter, d Circumference, c Area of a circle = 3.14 × radius 2 A = π×r 2 Area & Circumference of a Circle Circumference of a circle = 3.14 × diameter C = π×D = 2×π×r
  7. 7. Shape Area Triangle ½ ( L×W) Square L×W Rectangle L×W Parallelogram L × Height Trapezium (A + B) × Height 2 Circle  × r ²
  8. 8. To Find Area of Complicated Shapes <ul><li>Split them up into basic shapes </li></ul><ul><li>Work out the area of each bit separately </li></ul><ul><li>The add them altogether </li></ul>
  9. 9. Perimeters of Complicated Shapes <ul><li>Put a dot in one corner then go around the shape </li></ul><ul><li>Write down the length of every side as you go </li></ul><ul><li>Even sides that have no length given you need to work out </li></ul><ul><li>Keep going until you get to the dot </li></ul>6cm 20cm 14cm 10cm 8cm 10cm
  10. 10. Surface Area To find the surface area of a 3D shape, imagine it laid out as a net. Calculate the area of each side and then add them together.
  11. 11. Areas and Volumes of 3D Shapes <ul><li>The volume of a 3D shape is a measure of the amount of space it occupies </li></ul><ul><li>Typical units of measure are cubic centimetres (cm³) and cubic metres (m³) </li></ul>
  12. 12. Volume of a Cuboid This is also the same as the area of the rectangle on one end (cross section) multiplied by the length of the cuboid Volume of cuboid = length × width × height V = l × w × h
  13. 13. Volume of a Prism <ul><li>A prism is a 3D shape with the same cross section all along its length </li></ul><ul><li>To calculate the volume of the prism you need to find the area of the cross section and multiply it by the height or length </li></ul>Volume of prism = cross sectional area x length
  14. 14. Finding the Area of a Prism Volume of prism = Triangle area x length
  15. 15. Area and Volume Using formulae Take 2
  16. 16. Finding Area and Perimeter of a Square or Rectangle <ul><li>Area is the measure of the amount of space a shape covers </li></ul><ul><li>Perimeter is the distance all the way around the outside. </li></ul>Area of a rectangle = length × width A = l × w Perimeter = 2 × (length and width) length width
  17. 17. Finding Area of a Triangle <ul><li>A triangle takes up half the space of a rectangle with the same side lengths. </li></ul>length (base) width (height) Area of a triangle = ½ length × width A = ½ l×w
  18. 18. Length Perpendicular height Area of a parallelogram = length × perpendicular height A = l×h Finding Area of a Parallelogram
  19. 19. Perpendicular height Length a Length b Finding Area of a Trapezium Area of a trapezium = ½ (length a + length b) × perp height A = ½ (a+b) × h
  20. 20. Radius, r Diameter, d Circumference, c Area of a circle = 3.14 × radius 2 A = π×r 2 Area & Circumference of a Circle Circumference of a circle = 3.14 × diameter C = π×D = 2×π×r
  21. 21. Shape Area Triangle ½ ( L×W) Square L×W Rectangle L×W Parallelogram L × Height Trapezium (A + B) × Height 2 Circle  × r ²
  22. 22. To Find Area of Complicated Shapes <ul><li>Split them up into basic shapes </li></ul><ul><li>Work out the area of each bit separately </li></ul><ul><li>The add them altogether </li></ul>
  23. 23. Perimeters of Complicated Shapes <ul><li>Put a dot in one corner then go around the shape </li></ul><ul><li>Write down the length of every side as you go </li></ul><ul><li>Even sides that have no length given you need to work out </li></ul><ul><li>Keep going until you get to the dot </li></ul>6cm 20cm 14cm 10cm 8cm 10cm
  24. 24. Surface Area To find the surface area of a 3D shape, imagine it laid out as a net. Calculate the area of each side and then add them together.
  25. 25. Areas and Volumes of 3D Shapes <ul><li>The volume of a 3D shape is a measure of the amount of space it occupies </li></ul><ul><li>Typical units of measure are cubic centimetres (cm³) and cubic metres (m³) </li></ul>
  26. 26. Volume of a Cuboid This is also the same as the area of the rectangle on one end (cross section) multiplied by the length of the cuboid Volume of cuboid = length × width × height V = l × w × h
  27. 27. Volume of a Prism <ul><li>A prism is a 3D shape with the same cross section all along its length </li></ul><ul><li>To calculate the volume of the prism you need to find the area of the cross section and multiply it by the height or length </li></ul>Volume of prism = cross sectional area x length
  28. 28. Finding the Area of a Prism Volume of prism = Triangle area x length
  29. 29. Area and Volume Using formulae
  30. 30. Shape Area Triangle ½ ( L×W) Square L×W Rectangle L×W Parallelogram L × Perp Height Trapezium (A + B) × Height 2 Circle Area  × r ² Circle Circumference 2×  ×r or  ×D
  31. 31. ……………… . cm 2 (Total 2 marks)
  32. 32. ……………… . cm 2 (Total 4 marks)
  33. 33. ……………… . ……… (Total 3 marks)
  34. 34. (Total 4 marks)
  35. 35. ……………… . cm 2 (Total 3 marks)

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