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Polygon Area Calculation and Construction

Polygon Area Calculation and Construction
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2024-03-07 21:36
PolygonAngleGeometric Construction
This example demonstrates how to use GeoGebra to draw polygons and calculate their areas. The key mathematical concepts include the formula for polygon area, as well as calculations for special quadrilaterals like parallelograms, trapezoids, rhombuses, and squares. Construction points involve using the Polygon command to create shapes, Midpoint to find midpoints, and Angle to measure angles. Suitable for elementary students in grades 5-6 for geometry learning and classroom practice.

GeoGebra Commands & Parameters

  1. If(questionCount ≟ 1, 1, If[questionCount ≟ 2, 1, If[questionCount ≟ 3, 1, If[questionCount ≟ 4, 1, If[questionCount ≟ 5, 1, If[questionCount ≟ 6, 1, If[questionCount ≟ 7, 1, If[questionCount ≟ 8, 1, If[questionCount ≟ 9, 1, If[questionCount ≟ 10, 1]]]]]]]]]) → RO
  2. Corner(HinweisText, 2) → CornerHint2
  3. Corner(HinweisText, 3) → CornerHint3
  4. If(showanswer, "\bold{Lösung: }", "") → LoesungText
  5. Corner(Angabe, 1) → CornerAngabe
  6. Corner(HinweisText, 1) → CornerHint1
  7. If(tries ≠ 3, y(CornerHint3) - y(CornerHint2) - 0.15, y(Corner[SolutionText, 3]) - y(Corner[SolutionText, 2]) - 0.15) → heighthint
  8. RemoveUndefined({richtig1, If[RO > 1, richtig2], If[RO > 2, richtig3], If[RO > 3, richtig4], If[RO > 4, richtig5]}) → ListeRichtig
  9. RemoveUndefined({If[MCO ≟ 5 ∧ RO < 5 ∨ MCO ≟ 4 ∧ RO < 4 ∨ MCO ≟ 3 ∧ RO < 3, falsch1], If[MCO ≟ 5 ∧ RO < 4 ∨ MCO ≟ 4 ∧ RO < 3 ∨ MCO ≟ 3 ∧ RO < 2, falsch2], If[MCO ≟ 5 ∧ RO < 3 ∨ MCO ≟ 4 ∧ RO < 2, falsch3], If[MCO ≟ 5 ∧ RO < 2, falsch4]}) → ListeFalsch
  10. Union(ListeRichtig, ListeFalsch) → ListeAlle
  11. Shuffle(ListeAlle) → Reihenfolge, {"\textsf{wird 4-mal so groß.}", "\textsf{wird 16-mal so groß.}", "\textsf{wird 2-mal so groß.}", "\textsf{wird 8-mal so groß.}"}
  12. If(Reihenfolge(1) ∈ ListeRichtig, (("\math{" * Reihenfolge(1)) * "}\\\\"), "") → Loesungstext1
  13. If(Reihenfolge(2) ∈ ListeRichtig, (("\math{" * Reihenfolge(2)) * "}\\\\"), "") → Loesungstext2
  14. If(Reihenfolge(3) ∈ ListeRichtig, (("\math{" * Reihenfolge(3)) * "}\\\\"), "") → Loesungstext3
  15. If(Reihenfolge(4) ∈ ListeRichtig, (("\math{" * Reihenfolge(4)) * "}\\\\"), "") → Loesungstext4
  16. If(Reihenfolge(5) ∈ ListeRichtig, (("\math{" * Reihenfolge(5)) * "}\\\\"), "") → Loesungstext5
  17. Corner(Optionstext5, 3) → Corner53
  18. Corner(Optionstext5, 1) → Corner51
  19. Corner(Optionstext5, 2) → Corner52
  20. Corner(Optionstext4, 1) → Corner41
  21. Corner(Optionstext4, 2) → Corner42
  22. Corner(Optionstext3, 1) → Corner31
  23. Corner(Optionstext3, 2) → Corner32
  24. Corner(Optionstext2, 1) → Corner21
  25. Corner(Optionstext2, 2) → Corner22
  26. Corner(Optionstext1, 2) → Corner12
  27. Corner(Optionstext1, 1) → Corner11
  28. Max({x(Corner12) - x(Corner11), x(Corner22) - x(Corner21), x(Corner32) - x(Corner31), x(Corner42) - x(Corner41), x(Corner52) - x(Corner51)}) → maxwidth
  29. Corner(Optionstext4, 3) → Corner43
  30. Corner(Optionstext3, 3) → Corner33
  31. Corner(Optionstext2, 3) → Corner23
  32. Corner(Optionstext1, 3) → Corner13
  33. If(step < 3, Erklaerung2, "\\\textsf{ \large{\bold{. . .}}}") → ShowErkl2
  34. If(MCO ≥ 4, If[Reihenfolge(4) ∈ ListeRichtig ∧ option4 ≟ true ∨ Reihenfolge(4) ∈ ListeFalsch ∧ option4 ≟ false, true, false], true) → correct4
  35. If(correct4, 1, 0) → point4
  36. If(MCO ≟ 5, If[Reihenfolge(5) ∈ ListeRichtig ∧ option5 ≟ true ∨ Reihenfolge(5) ∈ ListeFalsch ∧ option5 ≟ false, true, false], true) → correct5
  37. If(correct5, 1, 0) → point5
  38. If(Reihenfolge(3) ∈ ListeRichtig ∧ option3 ≟ true ∨ Reihenfolge(3) ∈ ListeFalsch ∧ option3 ≟ false, true, false) → correct3
  39. If(correct3, 1, 0) → point3
  40. If(Reihenfolge(2) ∈ ListeRichtig ∧ option2 ≟ true ∨ Reihenfolge(2) ∈ ListeFalsch ∧ option2 ≟ false, true, false) → correct2
  41. If(correct2, 1, 0) → point2
  42. If(Reihenfolge(1) ∈ ListeRichtig ∧ option1 ≟ true ∨ Reihenfolge(1) ∈ ListeFalsch ∧ option1 ≟ false, true, false) → correct1
  43. If(correct1, 1, 0) → point1
  44. If(option1 ∨ option2 ∨ option3 ∨ option4 ∨ option5, (point1 + point2 + point3 + point4 + point5) / 5, 0) → score
  45. CountIf(x ≟ true, {option1, option2, option3, option4, option5}) → angekreuzt
  46. RoundBox(radius, Box1, height1, width) → box14, box11, box15, box12, box13
  47. RoundBox(radius, Box2, height2, width) → box24, box21, box25, box22, box23
  48. RoundBox(radius, Box3, height3, width) → box34, box31, box35, box32, box33
  49. RoundBox(radius, Box4, height4, width) → box44, box41, box45, box42, box43
  50. RoundBox(radius, Box5, height5, width) → box54, box51, box55, box52, box53
  51. If(step ≟ 3, "", step ≟ 1, ("\\\\" * Erklaerung3), "\\\textsf{ \large{\bold{. . .}}}") → ShowErkl3
  52. CountIf(x ≟ true, {correct1 ∧ option1, correct2 ∧ option2, correct3 ∧ option3, correct4 ∧ option4, correct5 ∧ option5}) → richtig
  53. If(correct, "✓ Richtig", "✘ Falsch") → CheckText
  54. If(tries ≠ 3, x(CornerHint2) - x(CornerHint1) - 0.15, x(Corner[SolutionText, 2]) - x(Corner[SolutionText, 1]) - 0.15) → widthhint
  55. RoundBox(radius, PosBoxHint, heighthint, widthhint) → boxh1, boxh2, boxh5, boxh3, boxh4
  56. Corner(Angabe, 4) → CornerAngabe2
  57. If(showsolution, Corner[LoesungswegText, 2] - (3, 1), (5, y(PosButton1))) → PosButton3
  58. SpeechBubbleRight(REF, 9.5, If[questionCount ≟ 4 ∨ questionCount ≟ 8 ∨ questionCount ≟ 9 ∨ questionCount ≟ 10, 2, 1.6]) → Vieleck1
  59. Segment(A_1, B_1) → f
  60. Midpoint(f) → C_1
  61. Vertex(box15, 6) → J_1
  62. Vertex(box15, 5) → K_1
  63. Vertex(box25, 5) → L_1
  64. Vertex(box25, 6) → M_1
  65. Vertex(box35, 5) → N_1
  66. Vertex(box35, 6) → O_1
  67. Vertex(box45, 5) → P_1
  68. Vertex(box45, 6) → Q_1
  69. Segment(K_1, J_1) → range1
  70. Segment(L_1, M_1) → range2
  71. Segment(N_1, O_1) → range3
  72. Segment(P_1, Q_1) → range4
  73. Midpoint(range1) → M1
  74. Midpoint(range2) → M2
  75. Midpoint(range3) → M3
  76. Midpoint(range4) → M4
  77. Polygon(R_1, S_1, T_1, U_1) → startRect, r_1, s_1, t_1, u_1
  78. SpeechBubbleLeft(PPP, 10, 2.7) → Vieleck2
  79. Segment(H_2, I_2) → g
  80. Segment(I_2, J_2) → h
  81. Segment(J_2, K_2) → i
  82. Segment(K_2, H_2) → j
  83. Point(j) → L_2
  84. Segment(I_2, L_2) → k
  85. Angle(K_2, L_2, I_2) → α

AI Drawing Prompt Reference

Draw a polygon to demonstrate how to calculate its area, including special quadrilaterals like parallelograms, trapezoids, rhombuses, and squares. Construct points to create shapes, find midpoints, and measure angles. Start by drawing the sides of the polygon, then mark midpoints and angles, and finally calculate and display the area of each shape.
The prompt above was compiled from the original drawing commands and is for reference only.