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Mixed Circle Task Bag: Area Calculation and Construction Exercise

Mixed Circle Task Bag: Area Calculation and Construction Exercise
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2024-12-19 16:42
In collections Kreis Umfang und Flächeninhalt
This example demonstrates how to calculate the area of circles, especially semicircles, quarter circles, and eighth circles through geometric construction. Key mathematical concepts include the area formula for circles, approximation methods, and geometric construction techniques. Construction points involve using GeoGebra commands such as Polygon, PointIn, IsInRegion to create circles and regions

GeoGebra Commands & Parameters

  1. Polygon(TüteBound1_{4}, TüteBound1_1, TüteBound1_2, TüteBound1_3) → TüteBound1, tütebound1_{4}, tütebound1_1, tütebound1_2, tütebound1_3
  2. PointIn(TüteBound1) → Zettel1Anchor_1
  3. Polygon(Zettel1Anchor_1, Zettel1Anchor_2, Zettel1Anchor_3, Zettel1Anchor_4) → Zettel1, zettel1anchor_1, zettel1anchor_2, zettel1anchor_3, zettel1anchor_4
  4. PointIn(TüteBound1) → Zettel2Anchor_1
  5. PointIn(TüteBound1) → Zettel3Anchor_1
  6. PointIn(TüteBound1) → Zettel4Anchor_1
  7. Polygon(Zettel2Anchor_1, Zettel2Anchor_2, Zettel2Anchor_3, Zettel2Anchor_4) → Zettel2, zettel2anchor_1, zettel2anchor_2, zettel2anchor_3, zettel2anchor_4
  8. Polygon(Zettel3Anchor_1, Zettel3Anchor_2, Zettel3Anchor_3, Zettel3Anchor_4) → Zettel3, zettel3anchor_1, zettel3anchor_2, zettel3anchor_3, zettel3anchor_4
  9. Polygon(Zettel4Anchor_1, Zettel4Anchor_2, Zettel4Anchor_3, Zettel4Anchor_4) → Zettel4, zettel4anchor_1, zettel4anchor_2, zettel4anchor_3, zettel4anchor_4
  10. Polygon(TüteBound2_1, TüteBound2_2, TüteBound2_3, TüteBound2_4) → TüteBound2, tütebound2_1, tütebound2_2, tütebound2_3, tütebound2_4
  11. PointIn(TüteBound2) → Zettel5Anchor_1
  12. PointIn(TüteBound2) → Zettel6Anchor_1
  13. PointIn(TüteBound2) → Zettel7Anchor_1
  14. PointIn(TüteBound2) → Zettel8Anchor_1
  15. Polygon(Zettel5Anchor_1, Zettel5Anchor_2, Zettel5Anchor_3, Zettel5Anchor_4) → Zettel5, zettel5anchor_1, zettel5anchor_2, zettel5anchor_3, zettel5anchor_4
  16. Polygon(Zettel6Anchor_1, Zettel6Anchor_2, Zettel6Anchor_3, Zettel6Anchor_4) → Zettel6, zettel6anchor_1, zettel6anchor_2, zettel6anchor_3, zettel6anchor_4
  17. Polygon(Zettel7Anchor_1, Zettel7Anchor_2, Zettel7Anchor_3, Zettel7Anchor_4) → Zettel7, zettel7anchor_1, zettel7anchor_2, zettel7anchor_3, zettel7anchor_4
  18. Polygon(Zettel8Anchor_1, Zettel8Anchor_2, Zettel8Anchor_3, Zettel8Anchor_4) → Zettel8, zettel8anchor_1, zettel8anchor_2, zettel8anchor_3, zettel8anchor_4
  19. Polygon(DecisionBound_1, DecisionBound_2, DecisionBound_3, DecisionBound_4) → DecisionArea, decisionbound_1, decisionbound_2, decisionbound_3, decisionbound_4
  20. IsInRegion(Zettel1Anchor_1, DecisionArea) → zettel1dec
  21. IsInRegion(Zettel2Anchor_1, DecisionArea) → zettel2dec
  22. IsInRegion(Zettel3Anchor_1, DecisionArea) → zettel3dec
  23. IsInRegion(Zettel4Anchor_1, DecisionArea) → zettel4dec
  24. IsInRegion(Zettel5Anchor_1, DecisionArea) → zettel5dec
  25. IsInRegion(Zettel6Anchor_1, DecisionArea) → zettel6dec
  26. IsInRegion(Zettel7Anchor_1, DecisionArea) → zettel7dec
  27. IsInRegion(Zettel8Anchor_1, DecisionArea) → zettel8dec
  28. Polygon(AngabeAnchor_1, AngabeAnchor_2, AngabeAnchor_3, AngabeAnchor_4) → Angabe, angabeanchor_1, angabeanchor_2, angabeanchor_3, angabeanchor_4
  29. Segment(UmrandungAnchor_1, UmrandungAnchor_2) → Umrandung_1
  30. Segment(UmrandungAnchor_2, UmrandungAnchor_{4}) → Umrandung_2
  31. Segment(UmrandungAnchor_{4}, UmrandungAnchor_3) → Umrandung_3
  32. Segment(UmrandungAnchor_3, UmrandungAnchor_1) → Umrandung_4
  33. Textfield(input1) → InputBox1
  34. Textfield(input2) → InputBox2
  35. Textfield(input3) → InputBox3
  36. If(aufgabeNum ≟ 1, Defined[input1], aufgabeNum ≟ 6, Defined[input6], aufgabeNum ≟ 7, Defined[input7], aufgabeNum ≟ 8, Defined[input8], false, aufgabeNum ≟ 2, Defined[input2], aufgabeNum ≟ 3, Defined[input3], aufgabeNum ≟ 4, Defined[input4], aufgabeNum ≟ 5, Defined[input5]) → fixed
  37. Segment(PosA1 + (0, (-dis)), PosA1 + (radius1, (-dis))) → seg11
  38. Segment(PosA1 + (radius1, (-dis)), PosA1 + ((2 * radius1), (-dis))) → seg12
  39. Segment(PosA1 + ((2 * radius1), (-dis)), PosA1 + ((3 * radius1), (-dis))) → seg13
  40. Segment(PosA1 + ((3 * radius1) + dis, 0), PosA1 + ((3 * radius1) + dis, (2 * radius1))) → seg14
  41. Textfield(input7) → InputBox7
  42. Segment(PosA7 + ((-2 * radius7), radius7 + dis), PosA7 + (0, radius7 + dis)) → seg71
  43. Segment(PosA7 + ((0 * radius7), radius7 + dis), PosA7 + ((2 * radius7), radius7 + dis)) → seg72
  44. Segment(PosA3 + ((-radius3), radius3 + dis), PosA3 + (0, radius3 + dis)) → seg31
  45. Segment(PosA3 + (0, radius3 + dis), PosA3 + (radius3, radius3 + dis)) → seg32
  46. Segment(PosA3 + (radius3 + dis, radius3), PosA3 + (radius3 + dis, 0)) → seg33
  47. Segment(PosA3 + (radius3 + dis, 0), PosA3 + (radius3 + dis, (-radius3))) → seg34
  48. Segment(PosA2 + (0, (-dis)), PosA2 + ((2 * radius2), (-dis))) → seg21
  49. Segment(PosA2 + ((2 * radius2) + dis, 0), PosA2 + ((2 * radius2) + dis, radius2 / 2)) → seg22
  50. Segment(PosA2 + ((2 * radius2) + dis, radius2 / 2 + radius2), PosA2 + ((2 * radius2) + dis, radius2 / 2)) → seg23
  51. Textfield(input5) → InputBox5
  52. Segment(PosA5 + ((0 * radius5), (-dis)), PosA5 + ((1 * radius5), (-dis))) → seg51
  53. Segment(PosA5 + ((1 * radius5), (-dis)), PosA5 + ((2 * radius5), (-dis))) → seg52
  54. Segment(PosA5 + ((2 * radius5), (-dis)), PosA5 + ((3 * radius5), (-dis))) → seg53
  55. Segment(PosA5 + ((3 * radius5) + dis, (0 * radius5)), PosA5 + ((3 * radius5) + dis, (1 * radius5))) → seg54
  56. Segment(PosA5 + ((3 * radius5) + dis, (1 * radius5)), PosA5 + ((3 * radius5) + dis, (2 * radius5))) → seg55
  57. Segment(PosA5 + ((3 * radius5) + dis, (2 * radius5)), PosA5 + ((3 * radius5) + dis, (3 * radius5))) → seg56
  58. Textfield(input4) → InputBox4
  59. Segment(PosA4 + (0, (-radius4) - dis), PosA4 + ((2 * radius4), (-radius4) - dis)) → seg41
  60. Segment(PosA4 + ((4 * radius4), (-radius4) - dis), PosA4 + ((2 * radius4), (-radius4) - dis)) → seg42
  61. Segment(PosA4 + ((4 * radius4) + dis, 0), PosA4 + ((4 * radius4) + dis, radius4)) → seg44
  62. Segment(PosA4 + ((4 * radius4) + dis, (-radius4)), PosA4 + ((4 * radius4) + dis, 0)) → seg43
  63. Textfield(input6) → InputBox6
  64. Segment(PosA6 + (0, (5 * radius6) + dis), PosA6 + ((0.25 * radius6), (5 * radius6) + dis)) → seg61
  65. Segment(PosA6 + ((0.25 * radius6), (5 * radius6) + dis), PosA6 + ((2.25 * radius6), (5 * radius6) + dis)) → seg62
  66. Segment(PosA6 + ((2.25 * radius6), (5 * radius6) + dis), PosA6 + ((2.75 * radius6), (5 * radius6) + dis)) → seg63
  67. Segment(PosA6 + ((2.75 * radius6), (5 * radius6) + dis), PosA6 + ((4.75 * radius6), (5 * radius6) + dis)) → seg64
  68. Segment(PosA6 + ((4.75 * radius6), (5 * radius6) + dis), PosA6 + ((5 * radius6), (5 * radius6) + dis)) → seg65
  69. Segment(PosA6 + ((5 * radius6) + dis, (5 * radius6)), PosA6 + ((5 * radius6) + dis, (5 * radius6) - (0.25 * radius6))) → seg66
  70. Segment(PosA6 + ((5 * radius6) + dis, (4.75 * radius6)), PosA6 + ((5 * radius6) + dis, (2.75 * radius6))) → seg67
  71. Segment(PosA6 + ((5 * radius6) + dis, (2.75 * radius6)), PosA6 + ((5 * radius6) + dis, (2.25 * radius6))) → seg68
  72. Segment(PosA6 + ((5 * radius6) + dis, (2.25 * radius6)), PosA6 + ((5 * radius6) + dis, (0.25 * radius6))) → seg69
  73. Segment(PosA6 + ((5 * radius6) + dis, (0.25 * radius6)), PosA6 + ((5 * radius6) + dis, (0 * radius6))) → seg610
  74. Segment(PosA8 + (0, (-dis)), PosA8 + ((5 / 9 * radius8), (-dis))) → seg81
  75. Segment(PosA8 + ((5 / 9 * radius8), (-dis)), PosA8 + (radius8 + (4 / 9 * radius8), (-dis))) → seg82
  76. Segment(PosA8 + (radius8 + (4 / 9 * radius8), (-dis)), PosA8 + ((2 * radius8), (-dis))) → seg83
  77. Segment(PosA8 + ((2 * radius8) + dis, 0), PosA8 + ((2 * radius8) + dis, radius8)) → seg84
  78. Textfield(input8) → InputBox8
  79. Text("\textsf{m²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit8
  80. Text("\textsf{cm²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit6
  81. Text("\textsf{m²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit5
  82. Text("\textsf{cm²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit1
  83. Text("\textsf{dm}", PosIB + (2.6, 0.15), false, true, 1, -1) → txtUnit7
  84. Text("\textsf{mm}", PosIB + (2.6, 0.1), false, true, 1, -1) → txtUnit2
  85. Text("\textsf{m²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit4
  86. Text("\textsf{dm²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit3