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Chpater 10 - Area & Perimeter

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Chpater 10 - Area & Perimeter

  1. 1. Perimeter & Area Chapter 10
  2. 2. Perimeter Perimeter - Distance AROUND a plane figureTo measure the PERIMETER of a plane figure, you have tomeasure the distance AROUND it.Explore:1. Run a piece of yarn around the perimeter of a book.Mark where you end. Cut the yarn.2. ESTIMATE the PERIMETER of the book by looking at theyarn (remember, your pinky is about an inch and yourforearm is about a food)3. Use a ruler to determine the EXACT PERIMETER of thebook, in inch and centimeter.
  3. 3. Perimeter of Polygons Perimeter - Distance AROUND a plane figureTo measure the PERIMETER of a plane figure, you need toknow the length and width of the polygonLength - how long the polygon isWidth - how wide the polygon is Length WidthTo find the perimeter, ADD the measurements of thesides.
  4. 4. Perimeter of a Polygon Find the PERIMETER of this book. 1. What shape is the book? 2. How many sides does it have? 3. What is the Length of the book? 4. What is the Width of the book?5. What MATH do you need to do to find the PERIMETER?
  5. 5. Perimeter of a Polygon Find the PERIMETER of this book. 1. What shape is the book? Rectangl e 2. How many sides does it have? 3. What is the Length of the book? 4. What is the Width of the book?5. What MATH do you need to do to find the PERIMETER?
  6. 6. Perimeter of a Polygon Find the PERIMETER of this book. 1. What shape is the book? Rectangl e 2. How many sides does it have? 4 sides 3. What is the Length of the book? 4. What is the Width of the book?5. What MATH do you need to do to find the PERIMETER?
  7. 7. Perimeter of a Polygon Find the PERIMETER of this book. 1. What shape is the book? Rectangl e 2. How many sides does it have? 4 sides 3. What is the Length of the 32 in book? 4. What is the Width of the book?5. What MATH do you need to do to find the PERIMETER?
  8. 8. Perimeter of a Polygon Find the PERIMETER of this book. 1. What shape is the book? Rectangl e 2. How many sides does it have? 4 sides 3. What is the Length of the 32 in book? 20 in 4. What is the Width of the book?5. What MATH do you need to do to find the PERIMETER?
  9. 9. Add!20 in + 32 in + 20 in + 32 in = 104 inches (don’t forgetto add all the sides!Multiply & Add!(20 in x 2) + (32 in x 2) = 40 in + 64 in = 104 inches
  10. 10. Lengt hAdd!20 in + 32 in + 20 in + 32 in = 104 inches (don’t forgetto add all the sides!Multiply & Add!(20 in x 2) + (32 in x 2) = 40 in + 64 in = 104 inches
  11. 11. Lengt h WidthAdd!20 in + 32 in + 20 in + 32 in = 104 inches (don’t forgetto add all the sides!Multiply & Add!(20 in x 2) + (32 in x 2) = 40 in + 64 in = 104 inches
  12. 12. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in
  13. 13. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in
  14. 14. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in
  15. 15. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in
  16. 16. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in
  17. 17. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in
  18. 18. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in +
  19. 19. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in +
  20. 20. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in + +
  21. 21. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in + +
  22. 22. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in + + +
  23. 23. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in + + +
  24. 24. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in + + + +
  25. 25. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in + + + +
  26. 26. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in + + + +
  27. 27. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in + + + +
  28. 28. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in + + + +
  29. 29. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in + + + +
  30. 30. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in+20 in + + + +
  31. 31. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in+20 in + + + +
  32. 32. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in+20 in 9 in + + + + +
  33. 33. PerimeterTry these:Find the PERIMETER of this polygon. 5 in 4 in 6 in 5 in 5 in 6 in 9 in 4 in 3 in 20 in 6 in+ 5 in 5 in 4 in 5 in 6 in+ 4 in+3 in+20 in 9 in + + + + = + 67in
  34. 34. Try Another...
  35. 35. Try Another...
  36. 36. Answer: 24 feet
  37. 37. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingTo measure the AREA of a plane figure, you have to countthe number of SQUARE UNITS that will fit inside it withoutover lapping. = 1 square unit How many could fit inside this rectangle?
  38. 38. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingTo measure the AREA of a plane figure, you have to countthe number of SQUARE UNITS that will fit inside it withoutover lapping. = 1 square unit How many could fit inside this rectangle?
  39. 39. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingTo measure the AREA of a plane figure, you have to countthe number of SQUARE UNITS that will fit inside it withoutover lapping. = 1 square unit How many could fit inside this rectangle? 24!
  40. 40. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingTo measure the AREA of a plane figure, you have to countthe number of SQUARE UNITS that will fit inside it withoutover lapping. = 1 square unit How many could fit inside this rectangle? 24! This rectangle is 24 SQUARE UNITS!
  41. 41. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingYou can also use a grid paper to estimate the area of afigure.
  42. 42. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingYou can also use a grid paper to estimate the area of afigure.
  43. 43. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingYou can also use a grid paper to estimate the area of afigure.You can place thefigure over the girdpaper.Count the numberof WHOLE squares.
  44. 44. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingYou can also use a grid paper to estimate the area of afigure.You can place thefigure over the girdpaper. * 1 *Count the number * 1 1 1 *of WHOLE squares. 1 1 1 1 1 * 1 1 1 * * 1 *
  45. 45. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingYou can also use a grid paper to estimate the area of afigure.You can place thefigure over the girdpaper. * 1 *Count the number * 1 1 1 * About 17of WHOLE squares. 1 1 1 1 1 Square * 1 1 1 * Units * 1 *
  46. 46. AreaArea - the number of SQUARE UNITS needed to cover thefigure without overlappingYou can also use a grid paper to estimate the area of afigure.You can place thefigure over the girdpaper. * 1 *Count the number * 1 1 1 * About 17of WHOLE squares. 1 1 1 1 1 SquareThen add thepartial squares * 1 1 1 * Units(*)together to * 1 *estimate!
  47. 47. Area for a SquareTo find the area of a Square, you just have to multiplythe length of the side by itself 4 in 4 in x 4 in = 14 square inch 4 in We have to say “square” inch because we ALWAYS measure AREA in SQUARE units!
  48. 48. Area of a SquareTry this. This square has sides that are 6 feet. Findthe AREA. 6 ft x 6 ft = 36 square feet Don’t forget the SQURE units!
  49. 49. Area of a RectangleTo find the area of a Rectangle, you just have tomultiply the LENGTH and the WIDTH.Area of the Rectangle = Length XWidthArea of this Rectangle =
  50. 50. Area of a RectangleTo find the area of a Rectangle, you just have tomultiply the LENGTH and the WIDTH. Length = 4 inchesArea of the Rectangle = Length XWidthArea of this Rectangle =
  51. 51. Area of a RectangleTo find the area of a Rectangle, you just have tomultiply the LENGTH and the WIDTH. Width = 6 inches Length = 4 inchesArea of the Rectangle = Length XWidthArea of this Rectangle =
  52. 52. Area of a RectangleTo find the area of a Rectangle, you just have tomultiply the LENGTH and the WIDTH. Width = 6 inches Length = 4 inchesArea of the Rectangle = Length XWidth 4 in x 6 in = 24 square inchesArea of this Rectangle =
  53. 53. Area of a RectangleTo find the area of a Rectangle, you just have tomultiply the LENGTH and the WIDTH. Width = 6 inches Length = 4 inchesArea of the Rectangle = Length XWidth 4 in x 6 in = 24 square inchesArea of this Rectangle = Don’t forget the SQURE units!
  54. 54. Area of a RectangleTo find the area of a Rectangle, you just have tomultiply the LENGTH and the WIDTH. Width = 6 inches Length = 4 inchesArea of the Rectangle = Length XWidth 4 in x 6 in = 24 square inchesArea of this Rectangle = Don’t forget the SQURE units!
  55. 55. Try This one...Find the Area of this Rectangle...
  56. 56. Try This one...Find the Area of this Rectangle... Length = 7 meters
  57. 57. Try This one...Find the Area of this Rectangle... Width = 3 meters Length = 7 meters
  58. 58. Try This one...Find the Area of this Rectangle... Width = 3 meters Length = 7 meters 7 in x 3 in = 21 square meters
  59. 59. Try This one...Find the Area of this Rectangle... Width = 3 meters Length = 7 meters 7 in x 3 in = 21 square meters Don’t forget the SQURE units!
  60. 60. Try This one...Find the Area of this Rectangle... Width = 3 meters Length = 7 meters 7 in x 3 in = 21 square meters Don’t forget the SQURE units!
  61. 61. Find the Pattern1.Determine the pattern. What will come next?2.Draw the next 3 figures until you get to the seventhfigure following the pattern.3.Determine how you would find the PERIMETER.
  62. 62. ?
  63. 63. The pattern was made 2inwith rectangles that are3 inches long and 2 3ininches wide.If the pattern iscontinued, what will bethe perimeter of the fifthfigure in the pattern?Challenge: What is theAREA?
  64. 64. The pattern was made 2inwith rectangles that are3 inches long and 2 3ininches wide. 2 + 2 + 2 + 2 + 3 + 3 = 14 inIf the pattern iscontinued, what will bethe perimeter of the fifthfigure in the pattern?Challenge: What is theAREA?
  65. 65. The pattern was made 2inwith rectangles that are3 inches long and 2 3ininches wide. 2 + 2 + 2 + 2 + 3 + 3 = 14 inIf the pattern iscontinued, what will bethe perimeter of the fifthfigure in the pattern? 2+2+2+2+2+2+3+3= 18 inChallenge: What is theAREA?
  66. 66. The pattern was made 2inwith rectangles that are3 inches long and 2 3ininches wide. 2 + 2 + 2 + 2 + 3 + 3 = 14 inIf the pattern iscontinued, what will bethe perimeter of the fifthfigure in the pattern? 2+2+2+2+2+2+3+3= 18 in 2+2+2+2+2+2+2+2+3+3 = 22 inChallenge: What is theAREA?
  67. 67. The pattern was made 2inwith rectangles that are3 inches long and 2 3ininches wide. 2 + 2 + 2 + 2 + 3 + 3 = 14 inIf the pattern iscontinued, what will bethe perimeter of the fifthfigure in the pattern? 2+2+2+2+2+2+3+3= 30 18 in INCHES 2+2+2+2+2+2+2+2+3+3 = 22 inChallenge: What is theAREA?
  68. 68. The pattern was made 2inwith rectangles that are3 inches long and 2 3ininches wide. 2 + 2 + 2 + 2 + 3 + 3 = 14 inIf the pattern iscontinued, what will bethe perimeter of the fifthfigure in the pattern? 2+2+2+2+2+2+3+3= 30 18 in INCHES 2+2+2+2+2+2+2+2+3+3 = 22 inChallenge: What is the 36AREA? INCHES
  69. 69. 4th figure5th figure
  70. 70. 4th figure5th figure
  71. 71. 4th figure 2+2+2+2+2+2+2+2+2+2+3+ 3 = 26 in5th figure
  72. 72. 4th figure 2+2+2+2+2+2+2+2+2+2+3+ 3 = 26 in5th figure
  73. 73. 4th figure 2+2+2+2+2+2+2+2+2+2+3+ 3 = 26 in5th figure
  74. 74. 4th figure 2+2+2+2+2+2+2+2+2+2+3+ 3 = 26 in5th figure2+2+2+2+2+2+2+2+2+2+2+2+3+3= 30 in Or (2x12) + (3x2) = 24 + 6 = 30 in
  75. 75. 4th figure 2+2+2+2+2+2+2+2+2+2+3+ 3 = 26 in 5th figure2+2+2+2+2+2+2+2+2+2+2+2+3+3= 30 in Or (2x12) + (3x2) = 24 + 6 = 30 inChallenge: What is theAREA?
  76. 76. 4th figure 2+2+2+2+2+2+2+2+2+2+3+ 3 = 26 in 5th figure 2+2+2+2+2+2+2+2+2+2+2+2+3+3= 30 in Or (2x12) + (3x2) = 24 + 6 = 30 in Challenge: What is the AREA?Length = 12 in, Width = 3 in:
  77. 77. 4th figure 2+2+2+2+2+2+2+2+2+2+3+ 3 = 26 in 5th figure2+2+2+2+2+2+2+2+2+2+2+2+3+3= 30 in Or (2x12) + (3x2) = 24 + 6 = 30 in Challenge: What is the AREA?Length = 12 in, Width = 3 in: x 3 in = 36 square Inches 12in
  78. 78. 4th figure 2+2+2+2+2+2+2+2+2+2+3+ 3 = 26 in 5th figure2+2+2+2+2+2+2+2+2+2+2+2+3+3= 30 in Or (2x12) + (3x2) = 24 + 6 = 30 in Challenge: What is the AREA?Length = 12 in, Width = 3 in: x 3 in = 36 square Inches 12in 36 SQUARE INCHES

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