Regular Polygons and Area

Regular Polygons and Area
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2016-05-13 03:10
This GeoGebra applet demonstrates regular polygons, their apothems, radii, and area calculations. By constructing regular polygons, midpoints, segments, angle bisectors, intersections, angles, and areas, students can visually understand the properties of regular polygons and their area calculations. Suitable for middle school and above students learning geometry and area calculations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly3, l, m, n, p, f_2, F, G, H
  2. Midpoint(f_2) → S_1
  3. Segment(S_1, F) → p_3
  4. Midpoint(m) → R_1
  5. Segment(R_1, H) → n_3
  6. Segment(A, B) → a
  7. Polygon(A, B, 3) → poly1, b, c, d, C
  8. Polygon(A, B, 4) → poly2, f, g, h, i, D, E
  9. Polygon(A, B, 6) → poly4, q, L, r, s, t, a_1, b_1, I, J, K
  10. Midpoint(a) → M
  11. AngularBisector(C, B, A) → c_1
  12. AngularBisector(B, A, C) → d_1
  13. AngularBisector(A, C, B) → e_1
  14. Intersect(e_1, d_1) → N
  15. Segment(N, B) → f_1
  16. Segment(N, A) → g_1
  17. Segment(N, C) → h_1
  18. Midpoint(d) → O
  19. Midpoint(c) → P
  20. Segment(N, P) → i_1
  21. Segment(N, O) → j_1
  22. Segment(M, N) → k_1
  23. Midpoint(a) → Q
  24. Midpoint(i) → R
  25. Midpoint(h) → S
  26. Midpoint(g) → T
  27. AngularBisector(E, D, B) → l_1
  28. AngularBisector(D, B, A) → m_1
  29. Intersect(l_1, m_1) → U
  30. Midpoint(h) → V
  31. Midpoint(i) → W
  32. Midpoint(g) → Z
  33. Midpoint(a) → A_1
  34. Segment(U, Z) → n_1
  35. Segment(U, V) → p_1
  36. Segment(U, W) → q_1
  37. Segment(U, A_1) → r_1
  38. Segment(U, B) → s_1
  39. Segment(U, D) → t_1
  40. Segment(U, E) → a_2
  41. Segment(U, A) → b_2
  42. Angle(M, N, B) → α
  43. Angle(N, B, A) → β
  44. Angle(a, k_1) → γ
  45. Angle(A_1, U, B) → δ
  46. Angle(U, B, A) → ε
  47. Intersect(r_1, a) → B_1
  48. Angle(B, B_1, U) → ζ
  49. Midpoint(a) → F_1
  50. Midpoint(a_1) → K_1
  51. Midpoint(b_1) → L_1
  52. Midpoint(a) → M_1
  53. Midpoint(r) → N_1
  54. Midpoint(s) → O_1
  55. Midpoint(t) → P_1
  56. AngularBisector(K, J, I) → p_2
  57. AngularBisector(J, I, B) → q_2
  58. Intersect(q_2, p_2) → Q_1
  59. Segment(Q_1, I) → r_2
  60. Segment(N_1, Q_1) → s_2
  61. Segment(Q_1, B) → t_2
  62. Segment(M_1, Q_1) → a_3
  63. Segment(Q_1, O_1) → c_3
  64. Segment(J, Q_1) → d_3
  65. Segment(Q_1, P_1) → e_3
  66. Segment(K, Q_1) → f_3
  67. Segment(Q_1, K_1) → g_3
  68. Segment(L, Q_1) → h_3
  69. Segment(Q_1, L_1) → i_3
  70. Angle(M_1, Q_1, B) → κ
  71. Angle(Q_1, B, M_1) → λ
  72. Angle(B, M_1, Q_1) → μ
  73. Segment(A, Q_1) → k
  74. Midpoint(f_2) → C_1
  75. Midpoint(p) → D_1
  76. Midpoint(n) → E_1
  77. Midpoint(m) → G_1
  78. Midpoint(b) → H_1
  79. Segment(H_1, G) → g_2
  80. Segment(F, C_1) → h_2
  81. Intersect(n_3, p_3) → I_1
  82. Segment(H_1, I_1) → i_2
  83. Segment(I_1, G_1) → j_2
  84. Segment(I_1, E_1) → k_2
  85. Segment(I_1, D_1) → l_2
  86. Segment(I_1, C_1) → m_2
  87. Segment(G, I_1) → n_2
  88. Segment(I_1, F) → c_2
  89. Segment(B, I_1) → d_2
  90. Segment(A, I_1) → e_2
  91. Segment(H, I_1) → j_3
  92. Angle(B, Q, I_1) → η
  93. Angle(Q, I_1, B) → θ
  94. Angle(I_1, B, Q) → ι
  95. Midpoint(b) → J_1
  96. Polygon(B, A, N) → poly5, k_3, l_3, m_3
  97. Area(poly5) → u_1
  98. Perimeter(poly1) → v_1
  99. Polygon(A, U, B) → poly6, b_3, a_4, u_2
  100. Perimeter(poly6) → o_2
  101. Polygon(A, I_1, B) → poly7, b_4, a_5, i_4
  102. Perimeter(poly3) → v_2
  103. Polygon(A, Q_1, B) → poly8, b_5, a_6, q_3
  104. Perimeter(poly4) → w_2

AI Drawing Prompt Reference

Draw a regular pentagon and mark the midpoints of its sides, connecting each midpoint to the corresponding vertex. Then draw a regular triangle and a square, marking the midpoints of their sides and connecting each midpoint to the corresponding vertex. Next, draw a regular hexagon and mark the midpoints of its sides, connecting each midpoint to the corresponding vertex. Finally, draw three angle bisectors that intersect at a point, and draw three line segments from this intersection point to the vertices of the regular triangle.
The prompt above was compiled from the original drawing commands and is for reference only.