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Trapezium Area Demonstration -- Dissection

Trapezium Area Demonstration -- Dissection
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2017-12-11 14:21
PolygonVectorGeometric Construction
In collections Mathematics Form 1
This example dynamically demonstrates the area calculation of a trapezium through geometric dissection. It involves core concepts like the area formula of a trapezium, geometric partitioning, and vector operations. GeoGebra commands and objects such as If, Line, DynamicCoordinates, Point, OrthogonalLine, Intersect, Midpoint, Segment, Polygon, Rotate, Circle, Angle, and Vector are utilized in the construction. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. If(abs(x(E) - x(A)) < 0.2, (x(A), y(E)), E) → Pm
  2. Line(A, xAxis) → a
  3. DynamicCoordinates(E, x(Pm), y(Pm)) → B
  4. Line(B, a) → b
  5. Point(a) → D
  6. OrthogonalLine(A, a) → c
  7. Intersect(b, c) → G
  8. If(abs(x(F) - x(D)) < 0.2, (x(D), y(B)), (x(F), y(B))) → Pm2
  9. DynamicCoordinates(F, x(Pm2), y(Pm2)) → C
  10. Midpoint(A, G) → H
  11. Line(H, a) → d
  12. Segment(B, A) → e
  13. Segment(A, D) → f
  14. Segment(D, C) → g
  15. Segment(C, B) → h
  16. Intersect(d, e) → K
  17. Intersect(d, g) → J
  18. Polygon(B, K, J, C) → poly1, b_1, i, j, c_1
  19. Polygon(A, D, J, K) → poly2, a_1, d_1, j_1, i_1
  20. Rotate(B, ((k * 180))°, J) → B'
  21. Rotate(K, ((k * 180))°, J) → K'
  22. Rotate(J, ((k * 180))°, J) → J'
  23. Rotate(C, ((k * 180))°, J) → C'
  24. Polygon(B', K', J', C') → poly1', b', k', j', c'
  25. Circle(G, n) → q
  26. Circle(A, n) → r
  27. Intersect(r, a) → I, L
  28. Intersect(q, b) → O, P
  29. Line(B, c) → e_1
  30. Line(C, c) → f_1
  31. Circle(B, n) → g_1
  32. Circle(C, n) → h_1
  33. Circle(D, n) → k_1
  34. Midpoint(O, I) → M
  35. Circle(M, n) → p
  36. Line(M, c) → l
  37. Intersect(p, l, 2) → N
  38. Intersect(p, l, 1) → Q
  39. Intersect(g_1, e_1, 2) → R
  40. Intersect(h_1, f_1, 2) → S
  41. Midpoint(R, S) → T
  42. Line(T, a) → m
  43. Circle(T, n) → s
  44. Intersect(s, m, 1) → U
  45. Intersect(s, m, 2) → V
  46. Line(D, c) → t
  47. Intersect(r, c, 1) → W
  48. Intersect(k_1, t, 1) → Z
  49. Midpoint(W, Z) → A_1
  50. Line(A_1, a) → l_1
  51. Circle(A_1, n) → p_1
  52. Intersect(p_1, l_1, 1) → B_1
  53. Intersect(p_1, l_1, 2) → C_1
  54. Intersect(k_1, t, 2) → D_1
  55. Intersect(r, c, 2) → E_1
  56. Midpoint(E_1, D_1) → F_1
  57. Circle(F_1, n) → q_1
  58. Line(F_1, l_1) → m_1
  59. Intersect(q_1, m_1, 1) → G_1
  60. Intersect(q_1, m_1, 2) → H_1
  61. Intersect(h_1, f_1, 1) → I_1
  62. Intersect(g_1, e_1, 1) → J_1
  63. Midpoint(J_1, I_1) → K_1
  64. Circle(K_1, n) → r_1
  65. Line(K_1, l_1) → n_1
  66. Intersect(r_1, n_1, 2) → L_1
  67. Intersect(r_1, n_1, 1) → M_1
  68. If(BTop ≟ true, Vector[V, S], Vector[L_1, I_1]) → u_1
  69. If(BTop ≟ true, Vector[U, R], Vector[M_1, J_1]) → u_2
  70. If(BTop ≟ true, Vector[C_1, Z], Vector[H_1, D_1]) → v_1
  71. If(BTop ≟ true, Vector[B_1, W], Vector[G_1, E_1]) → v_2
  72. If(BTop ≟ true, Vector[N, O], Vector[Q, O]) → w_1
  73. If(BTop ≟ true, Vector[Q, I], Vector[N, I]) → w_2
  74. Angle(D, A, B) → α
  75. Angle(C, D, A) → β
  76. Intersect(a, e_1) → N_1
  77. Circle(N_1, n) → s_1
  78. Intersect(d, e_1) → O_1
  79. Intersect(s_1, a, 1) → P_1
  80. Intersect(g_1, b, 1) → Q_1
  81. Line(Q_1, P_1) → t_1
  82. Intersect(d, t_1) → R_1
  83. Circle(R_1, n) → c_2
  84. Intersect(c_2, t_1, 1) → S_1
  85. Intersect(c_2, t_1, 2) → T_1
  86. Vector(T_1, P_1) → v
  87. Vector(S_1, Q_1) → u
  88. SelectedIndex(Bahasa) → nn
  89. If(nn ≟ 1, "Derive the formula to calculate", "Menerbit rumus untuk menghitungkan") → Tex1
  90. If(nn ≟ 1, "the area of a trapezium", "luas bentuk trapezium") → Tex2