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Comparison of Hexagonal Prism and Triangular Prism

Comparison of Hexagonal Prism and Triangular Prism
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2020-02-22 22:09
PolygonSolid Geometry
This example demonstrates the geometric construction and volume calculation of a hexagonal prism and a triangular prism. It involves key concepts from polygons, triangles, and solid geometry. Using GeoGebra commands such as Polygon and Prism, the construction process of the prisms can be dynamically shown. Suitable for middle and high school students learning geometry and volume calculation.

GeoGebra Commands & Parameters

  1. Polygon(C, D, 3) → poly1, f, g, h_5, E
  2. Midpoint(E, D) → F
  3. Midpoint(C, E) → G
  4. Distance(C, D) → distanceCD
  5. Distance(C, D) → a
  6. Segment(K, F) → i
  7. Point(i) → H
  8. Circle(K, (0.5 * Distance[K, H])) → c
  9. Point(c) → J
  10. Mirror(J, K) → J'
  11. Circle(J, H) → d
  12. Intersect(d, f, 2) → I
  13. Mirror(H, K) → H'
  14. Circle(I, Distance[D, F]) → e
  15. Intersect(e, f, 1) → L
  16. Circle(J, I) → k
  17. Segment(K, L) → j
  18. Intersect(k, j, 1) → M
  19. Mirror(M, K) → M'
  20. Polygon(M, I, 3) → poly2, l, m, n, N
  21. Polygon(H', M', 3) → poly3, p, q, r, P
  22. Distance(N, H) → b
  23. Polygon(D, I, J, H, F) → poly4, d_1, i_1, j_1, h_1, f_1
  24. Polygon(H, J, K) → poly5, k_1, h_2, j_2
  25. Polygon(J', M', K) → poly6, k_2, j', m'
  26. Polygon(J, M, K) → poly7, k_3, j_3, m_1
  27. Polygon(L, M, J, I) → poly8, l_1, m_2, j_4, i_2
  28. Polygon(H', J', K) → poly9, k_4, h', j'_1
  29. Distance(G, P) → o
  30. Polygon(C, G, J', H', L) → poly10, c_1, g_1, j'_2, h'_1, l_2
  31. Polygon(E, F, M', J', G) → poly11, e_1, f_2, m'_1, j'_3, g_2
  32. Line(D, C) → s
  33. Point(s) → O
  34. Point(s) → Q
  35. Polygon(O, Q, 6) → poly12, t, U, n_1, p_1, q_1, r_1, s_1, R, S, T
  36. Point(s) → V
  37. Point(Circle[V, Segment[O, Q]]) → W
  38. Rotate(W + (Segment[Q, R], 0), Angle[R - Q] + Angle[W - V] - Angle[Q - O], W) → Z
  39. Rotate(Z + (Segment[R, S], 0), Angle[S - R] + Angle[Z - W] - Angle[R - Q], Z) → A_1
  40. Rotate(A_1 + (Segment[S, T], 0), Angle[T - S] + Angle[A_1 - Z] - Angle[S - R], A_1) → B_1
  41. Rotate(B_1 + (Segment[T, U], 0), Angle[U - T] + Angle[B_1 - A_1] - Angle[T - S], B_1) → C_1
  42. Polygon(V, W, Z, A_1, B_1, C_1) → poly13, v, w, z_1, a_1, b_1, c_2
  43. Vector(J', V) → u_1
  44. Rotate(E_1, (((-u) * 7.95))°, D_1) → I_1
  45. Rotate(H_1, (((-u) * 7.95))°, D_1) → J_1
  46. Rotate(F_1, (((-u) * 7.95))°, D_1) → K_1
  47. Rotate(G_1, (((-u) * 7.95))°, D_1) → L_1
  48. Polygon(L_1, J_1, I_1, D_1, K_1) → poly14, l_3, j_5, i_3, d_2, k_5
  49. Rotate(D_1, (-Angle[C, G, J']), K_1) → M_1
  50. Ray(K_1, M_1) → t_1
  51. Circle(K_1, Distance[G, C]) → e_2
  52. Intersect(e_2, t_1, 1) → N_1
  53. Rotate(K_1, (-(60°)), N_1) → O_1
  54. Ray(N_1, O_1) → n_2
  55. Circle(N_1, Distance[C, L]) → p_2
  56. Intersect(p_2, n_2, 1) → P_1
  57. Rotate(K_1, Angle[G, J', H'], D_1) → Q_1
  58. Ray(D_1, Q_1) → q_2
  59. Circle(D_1, Distance[J', H']) → r_2
  60. Rotate(N_1, (((-u) * 180))°, K_1) → R_1
  61. Rotate(P_1, (((-u) * 180))°, K_1) → S_1
  62. Rotate(Q_1, (((-u) * 180))°, K_1) → T_1
  63. Rotate(D_1, (((-u) * 180))°, K_1) → U_1
  64. Polygon(K_1, U_1, T_1, S_1, R_1) → poly15, k_6, u_2, t_2, s_2, r_3
  65. Rotate(T_1, Angle[H', J', K], U_1) → V_1
  66. Ray(U_1, V_1) → a_2
  67. Circle(U_1, Distance[J', K]) → c_3
  68. Intersect(c_3, a_2, 1) → W_1
  69. Rotate(W_1, (((-u) * 180))°, T_1) → Z_1
  70. Rotate(U_1, (((-u) * 180))°, T_1) → A_2
  71. Polygon(T_1, A_2, Z_1) → poly16, z_2, t_3, a_3
  72. Rotate(T_1, Angle[M, K, J], Z_1) → B_2
  73. Ray(Z_1, B_2) → b_2
  74. Circle(Z_1, Distance[K, J]) → d_3
  75. Intersect(d_3, b_2, 1) → C_2
  76. Circle(Z_1, Distance[K, M]) → e_3
  77. Intersect(e_3, a_3, 1) → D_2
  78. Rotate(C_2, ((u * 180))°, Z_1) → E_2
  79. Rotate(D_2, ((u * 178))°, Z_1) → F_2
  80. Polygon(E_2, F_2, Z_1) → poly17, z_3, e_4, f_3
  81. Rotate(F_2, Angle[M, J, I], E_2) → G_2
  82. Ray(E_2, G_2) → g_3
  83. Circle(E_2, Distance[J, I]) → h_3
  84. Rotate(I_1, Angle[H, F, D], J_1) → H_2
  85. Ray(J_1, H_2) → m_3
  86. Circle(J_1, Distance[F, D]) → p_3
  87. Intersect(p_3, m_3, 1) → I_2
  88. Rotate(J_1, 60°, I_2) → J_2
  89. Ray(I_2, J_2) → n_3
  90. Circle(I_2, Distance[D, I]) → q_3
  91. Intersect(q_3, n_3, 1) → K_2
  92. Rotate(I_2, Angle[D, I, J], K_2) → L_2
  93. Ray(K_2, L_2) → s_3
  94. Circle(K_2, Distance[I, J]) → c_4
  95. Intersect(c_4, s_3, 1) → M_2
  96. Rotate(I_2, ((u * 180))°, J_1) → Q_2
  97. Rotate(K_2, Angle[I, J, H], M_2) → N_2
  98. Rotate(I_2, ((u * 180))°, J_1) → O_2
  99. Rotate(K_2, ((u * 180))°, J_1) → P_2
  100. Rotate(M_2, ((u * 180))°, J_1) → R_2
  101. Rotate(N_2, ((u * 180))°, J_1) → S_2
  102. Polygon(O_2, P_2, R_2, S_2, J_1) → poly18, o_2, p_4, r_4, s_4, j_6
  103. Rotate(R_2, Angle[J, I, L], P_2) → T_2
  104. Ray(P_2, T_2) → b_3
  105. Circle(P_2, Distance[I, L]) → d_4
  106. Intersect(d_4, b_3, 1) → U_2
  107. Rotate(P_2, Angle[I, L, M], U_2) → V_2
  108. Ray(U_2, V_2) → f_4
  109. Circle(U_2, Distance[L, M]) → g_4
  110. Intersect(g_4, f_4, 1) → W_2
  111. Polygon(P_2, U_2, W_2, R_2) → poly19, p_5, u_3, w_2, r_5
  112. Rotate(U_2, ((u * 180))°, P_2) → Z_2
  113. Rotate(W_2, ((u * 180))°, P_2) → A_3
  114. Rotate(R_2, ((u * 180))°, P_2) → B_3
  115. Polygon(Z_2, A_3, B_3, P_2) → poly20, z_4, a_4, b_4, p_6
  116. Rotate(S_2, Angle[H, J, K], R_2) → C_3
  117. Ray(R_2, C_3) → h_4
  118. Circle(R_2, Distance[K, J]) → q_4
  119. Intersect(q_4, h_4) → D_3,
  120. Rotate(D_3, (((-u) * 180))°, S_2) → E_3
  121. Rotate(R_2, (((-u) * 180))°, S_2) → F_3
  122. Polygon(S_2, F_3, E_3) → poly21, e_5, s_5, f_5
  123. Rotate(S_2, Angle[M', K, J'], E_3) → G_3
  124. Ray(E_3, G_3) → i_4
  125. Circle(E_3, Distance[K, J']) → t_4
  126. Intersect(t_4, i_4, 1) → H_3
  127. Circle(E_3, Distance[K, M']) → c_5
  128. Intersect(c_5, f_5, 1) → I_3
  129. Rotate(H_3, ((u * 180))°, E_3) → J_3
  130. Rotate(I_3, ((u * 180))°, E_3) → K_3
  131. Polygon(J_3, E_3, K_3) → poly22, k_7, j_7, e_6
  132. Polygon(E_2, A_3, Z_1) → poly23, z_5, e_7, a_5
  133. Prism(poly15, h) → o_1, L_3, face1, face6, arête1, arête5, arête4, arête3, arête2, arête6, arête8, arête9, M_3, arête10, arête7, N_3, O_3, P_3, face2, face5, face4, face3
  134. Prism(poly18, h) → v_1, Q_3, face7, face12, arête12, arête13, arête14, arête15, arête11, arête16, arête18, arête19, R_3, arête20, arête17, S_3, T_3, U_3, face9, face10, face11, face8
  135. Prism(poly20, h) → w_1, V_3, arête22, arête23, arête24, arête21, arête25, arête27, arête28, arête26, W_3, Z_3, A_4, face15, face16, face14, face13, face17
  136. Prism(poly16, h) → v_2, B_4, arête30, arête32, arête34, arête33, C_4, D_4, face20, face21, face19, face18, arête29, arête31
  137. Prism(poly17, h) → o_3, E_4, arête35, arête38, arête40, arête39, F_4, G_4, face25, face24, face23, face22, arête36, arête37
  138. Prism(poly21, h) → v_3, H_4, arête42, arête44, arête46, arête45, I_4, J_4, face28, face29, face27, face26, arête41, arête43
  139. Prism(poly22, h) → w_3, K_4, arête49, arête50, arête52, arête51, L_4, M_4, face31, face32, face33, face30, arête48, arête47
  140. Prism(poly14, h) → l_4, N_4, face38, face39, arête57, arête55, arête54, arête53, arête56, arête58, arête60, arête61, O_4, arête62, arête59, P_4, Q_4, R_4, face37, face36, face34, face35

AI Drawing Prompt Reference

Draw a hexagonal prism and a triangular prism to demonstrate their geometric construction and volume calculation. Start by creating a hexagonal base and extending it upward to form the hexagonal prism, while also constructing the triangular prism. Label key points, edges, and faces, such as the vertices and midpoints of the hexagon and triangle, and the side lengths. Use different colors to distinguish the two prisms and annotate their volume formulas.
The prompt above was compiled from the original drawing commands and is for reference only.