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梯形面积演示——分割法

梯形面积演示——分割法
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2017-12-11 14:21
多边形向量几何作图
所属专题 Mathematics Form 1
①本范例通过动态分割梯形演示其面积计算方法；②涉及核心数学概念包括梯形面积公式、几何分割、向量运算；③构造中运用了If、Line、DynamicCoordinates、Point、OrthogonalLine、Intersect、Midpoint、Segment、Polygon、Rotate、Circle、Angle、Vector等GeoGebra命令与对象；④适合高中数学教学及几何作图学习。

GeoGebra 命令及参数

  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