perimeter, area volume

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perimeter, area volume

  1. 1. Ra Measuring Shape and Space This powerpoint is intended to be read in stages at the reader’s own pace. The main emphasis is to help adults understand Perimeter, Area & Volume
  2. 2. Units of Measurement When we measure distances we use whole metres or parts of metres (centimetres or millimetres) Some people might use yards or parts of yards (feet and inches) We will concentrate on Metric units
  3. 3. Perimeter The distance around a shape! Shape 1 Shape 2 6cm 5cm 10cm 5cm 8cm
  4. 4. Working out Shape 1 is a rectangle, what is its perimeter? Shape 2 is a Trapezium, what is its perimeter?
  5. 5. Perimeter Not all sides are labelled – These need to be worked out! 20 cm 32 cm 15cm 6 cm 5cm 5cm
  6. 6. Working out What is the Perimeter of the shape on the previous Slide?
  7. 7. Area Squared Units We measure flat surfaces In square units so we must know how wide A shape is and how high = one square unitIf Then this square has fifteen rows and Fifteen columns of unit squares So the area of the large square Is 15 x 15 = 225 units 2
  8. 8. Area
  9. 9. Working out 2 2 2 2 = 1 x 1 = 1 unit = 2 x 2 = 4 unit = 3 x 3 = 9 unit = 4 x 4 = 16unit 2 2 2 2
  10. 10. Volume Cubed units
  11. 11. Working out On the previous slide we could fit three and a half unit cubes horizontally, we could fit three and a half vertically and we could fit three and a half from front to back. So we have measured in three directions (Dimensions). If we now multiply these dimensions together we get 3.5x3.5x3.5= 42.875 units3
  12. 12. Circles What do we call the distance from the centre to the outside of a circle? RADIUS
  13. 13. Circles The Distance all the way across a circle is the DIAMETER The diameter is double the radius
  14. 14. Circumference • The Circumference is the distance all the way round the outside of a circle. • This is another name for the Perimeter of a Circle
  15. 15. Circumference • The Circumference is the distance all the way round the outside of a circle. • A larger Circle will have a larger Circumference (So the bigger the Radius; the bigger the Circumference!)
  16. 16. Calculating the Circumference Let’s consider the circle below, and say that it has a Radius that measures 10metres RADIUS Do you Know a Formula that we can use to calculate The Circumference?
  17. 17. Formulas for Circumference • Circumference= 2 x x Radius • Or C= 2 r • Or C= d • (Because 2r= diameter=d) • is a special number for Circles= 3.14
  18. 18. Working out
  19. 19. Calculating the Circumference Let’s consider the circle below, and say that it has a Radius that measures 10metres Do you Know a Formula that we can use to calculate The Circumference? C= 2 r So we can now calculate the Circumference C= 2 x 3.14 x 10 = 62.8m
  20. 20. Calculating the Area of a Circle Let’s consider the circle below, and say that it has a Radius that measures 10metres RADIUS The Area here is the flat surface coloured blue. Do you know a formula that we can use to calculate The Area?
  21. 21. Formula for the Area of a Circle • Area = x Radius squared • Or A= r Remember to do r x r first then x is a special number for Circles= 3.14 2
  22. 22. Working out
  23. 23. Calculating the Area of a Circle Let’s consider the circle below, and say that it has a Radius that measures 10metres rA= 2 So Here Area= 3.14 x (10 x 10) A= 314m 2
  24. 24. Area of a circle • Now you practice with these circles 1 2 3 Area when diameter is 30 cm Circumference of a circle radius = 35 metres Area when diameter is 20 inches You can use a calculator if you like! Or say = 3
  25. 25. Composite shapes • A composite shape is one that is constructed from two or more different shapes • These different shapes could be a combination of Rectangles, Circles, Squares, or Triangles. • All flat shapes will have a perimeter and some area
  26. 26. Example of A Composite Shape What in formation do you need?
  27. 27. Working out
  28. 28. Example of A Composite Shape We now know the area of the rectangle= 16x3 cm= 48 cm 3cm 16 cm 2
  29. 29. Example of A Composite Shape We can now see the two triangles are the same size so their combined area is the same as a rectangle 3cm x4cm= 12cm 4 cm 4 cm 2 3cm
  30. 30. Example of A Composite Shape Let’s calculate the area of the large half Circle then take away the area of the small half circle So far our Area running total is 48+ 12 cm2 3 cm8 cm
  31. 31. Working out
  32. 32. Example of A Composite Shape Area of Large = 0.5 x x (8x8) = 0.5x3.14 x 64 = 100.48cm 3 cm8 cm 2 Area of small = 0.5 x x (3x3) = 0.5x3.14 x 9 = 14.13cm 2 Area shaded Blue= 100.48-14.13= 86.35 cm
  33. 33. Example of A Composite Shape So we now have a total Area = 48+12+86.35= 146.35 cm 2
  34. 34. Formulas for Area Area of Rectangle or Square = Length X Width Area of a Triangle = ½ X Base X Height

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