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Reasoning to Find Area

Reasoning to Find Area
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2020-07-15 21:16
Polygon
This example demonstrates how to find area through geometric reasoning. Key mathematical concepts include polygons and area calculation. It uses commands like Segment, Polygon, CustomOctagon, Point, etc. Suitable for middle school and above students to learn geometric construction and area calculation.

GeoGebra Commands & Parameters

  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. CustomOctagon(E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2) → poly7, f_5, g_5, h_5, i_5, j_5, k_5, l_5, m_5
  62. CustomOctagon(M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2) → poly8, n_5, p_5, q_5, r_5, s_5, t_5, a_5, b_5
  63. Point(t_5) → V_2
  64. Point(n_5) → A_3
  65. CustomNonagon(U_2, P_2, V_2, W_2, R_2, Z_2, A_3, T_2, B_3) → c_5, d_5, e_5, f_6, g_6, h_6, i_6, j_6, k_6, poly9
  66. CustomPentagon(C_3, D_3, E_3, F_3, G_3) → l_6, m_6, n_6, p_6, q_6, poly10
  67. Point(b_5) → H_3
  68. Point(j_6) → I_3
  69. Segment(H_3, I_3) → r_6
  70. Point(a_5) → J_3
  71. Point(g_6) → K_3
  72. Segment(J_3, K_3) → s_6

AI Drawing Prompt Reference

Draw a geometric figure composed of multiple polygons, including a triangle, a quadrilateral, a pentagon, a hexagon, and an octagon. These polygons are connected by line segments, forming a complex combined shape. Start with the triangle, then sequentially add the quadrilateral, pentagon, hexagon, and octagon, with each polygon connected to others by line segments, ultimately forming a continuous geometric structure.
The prompt above was compiled from the original drawing commands and is for reference only.