IM 6.1.3 推理求面积:活动 2 与 3

IM 6.1.3 推理求面积:活动 2 与 3
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2020-08-26 22:26
① 这个范例演示如何通过分解与重组多边形(六边形、三角形、四边形)来推理并计算其面积。② 涉及的核心数学概念包括多边形面积公式、三角形面积、平行四边形面积、图形分割与拼合的几何推理。③ 作图要点:使用了 GeoGebra 命令 Segment(线段)、Polygon(多边形)、CustomHexagon、CustomTriangle、CustomQuadrilateral 以及 Point(点)来构建顶点 A、B、C、D、E、F、G、H、I、J、K、L、M 等对象,并生成多个多边形对象 poly1、h_1、i_1 等。④ 适合初中几何课程(六年级至八年级)作为面积推理教学演示,也可用于教师备课或学生自主探究。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Polygon(A, C, B) → t1, b, a, c
  5. Segment(D, E) → i
  6. Segment(E, F) → j
  7. Segment(F, G) → k
  8. Segment(G, D) → l
  9. Polygon(D, E, F, G) → q1, d, e, f_1, g_1
  10. Segment(H, I) → m
  11. Segment(I, J) → n
  12. Segment(J, K) → p
  13. Segment(K, L) → q
  14. Segment(L, H) → r
  15. Polygon(H, I, J, K, L) → poly1, h_1, i_1, j_1, k_1, l_1
  16. Segment(M, N) → s
  17. Segment(N, O) → t
  18. Segment(O, P) → m_1
  19. Segment(P, Q) → n_1
  20. Segment(Q, R) → p_1
  21. Segment(R, M) → q_1
  22. Polygon(R, M, N, O, P, Q) → poly2, r_1, m_2, n_2, o, p_2, q_2
  23. Segment(S, T) → s_1
  24. Segment(T, U) → t_1
  25. Segment(U, V) → a_1
  26. Segment(V, W) → b_1
  27. Segment(W, Z) → c_1
  28. Segment(Z, A_1) → d_1
  29. Segment(A_1, S) → e_1
  30. Polygon(S, T, U, V, W, Z, A_1) → poly3, s_2, t_2, u, v, w, z_1, f_2
  31. Segment(B_1, C_1) → g_2
  32. Segment(C_1, D_1) → h_2
  33. Segment(D_1, E_1) → i_2
  34. Segment(E_1, F_1) → j_2
  35. Segment(F_1, G_1) → k_2
  36. Segment(G_1, H_1) → l_2
  37. Segment(H_1, I_1) → r_2
  38. Segment(I_1, B_1) → a_2
  39. Polygon(B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1) → poly4, b_2, c_2, d_2, e_2, f_3, g_3, h_3, i_3
  40. Segment(J_1, K_1) → j_3
  41. Segment(K_1, L_1) → k_3
  42. Segment(L_1, M_1) → l_3
  43. Segment(M_1, N_1) → m_3
  44. Segment(N_1, O_1) → n_3
  45. Segment(O_1, P_1) → p_3
  46. Segment(P_1, Q_1) → q_3
  47. Segment(Q_1, R_1) → r_3
  48. Segment(R_1, J_1) → s_3
  49. Polygon(R_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1) → poly5, t_3, a_3, b_3, c_3, d_3, e_3, o_1, f_4, g_4
  50. Segment(S_1, T_1) → h_4
  51. Segment(T_1, U_1) → i_4
  52. Segment(U_1, V_1) → j_4
  53. Segment(V_1, W_1) → k_4
  54. Segment(W_1, Z_1) → l_4
  55. Segment(Z_1, A_2) → m_4
  56. Segment(A_2, B_2) → n_4
  57. Segment(B_2, C_2) → p_4
  58. Segment(C_2, D_2) → q_4
  59. Segment(D_2, S_1) → r_4
  60. Polygon(S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2) → poly6, s_4, e_4, t_4, u_1, v_1, w_1, a_4, b_4, c_4, d_4
  61. CustomHexagon(E_2, F_2, G_2, H_2, I_2, J_2) → f_5, g_5, h_5, i_5, j_5, k_5, poly7
  62. CustomTriangle(S_2, T_2, U_2) → a_5, b_5, c_5, t2
  63. CustomTriangle(T_2, V_2, W_2) → d_5, e_5, f_6, t3
  64. CustomTriangle(W_2, Z_2, A_3) → g_6, h_6, i_6, t4
  65. CustomTriangle(A_3, B_3, U_2) → j_6, k_6, l_6, t5
  66. CustomQuadrilateral(C_3, D_3, E_3, F_3) → q4, m_6, n_6, p_6, q_6
  67. CustomHexagon(G_3, H_3, I_3, J_3, K_3, L_3) → r_6, s_6, t_6, a_6, b_6, c_6, poly8
  68. Point(c_6) → M_3
  69. CustomHexagon(I_3, M_3, N_3, O_3, P_3, Q_3) → d_6, e_6, f_7, g_7, h_7, i_7, poly9
  70. Point(d_6) → S_3
  71. Segment(R_3, S_3) → l_5
  72. Segment(R_3, T_3) → m_5

AI 绘图提示语参考

请绘制一个由多个几何图形组成的复杂图形,包括三角形、四边形和七边形。这些图形通过线段连接,形成一个整体结构。图形中的各个部分可以进行分解和重组,以展示面积计算的方法。确保图形清晰可见,便于理解几何关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。