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Area of an Octagon

Area of an Octagon
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2023-03-13 04:20
PolygonSolid GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates how to calculate the area of an octagon. It involves core geometric concepts, including the calculation of the area of a polygon. The construction points include using GeoGebra commands: Circle, Rotate, Polygon, Mirror, and objects: A, B, c, N, a, C, P, c_1, a_1, b, d, z, A'、B'、C'、P'、c'、a'、b'、A''、B''、C''、P''、c''、a''、b''、A'''、B'''、C'''、P'''、c'''、a'''、b'''、A''''、B''''、C''''、P''''、c''''、a''''、b''''。It is suitable for middle school mathematics and geometry.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Rotate(B, a, A) → C
  3. Polygon(A, B, C) → P, c_1, a_1, b
  4. Rotate(A, z, B) → A'
  5. Rotate(B, z, B) → B'
  6. Rotate(C, z, B) → C'
  7. Polygon(A', B', C') → P', c', a', b'
  8. Mirror(A', b') → A''
  9. Mirror(B', b') → B''
  10. Mirror(C', b') → C''
  11. Polygon(A'', B'', C'') → P'', c'', a'', b''
  12. Rotate(A'', z, C') → A'''
  13. Rotate(B'', z, C') → B'''
  14. Rotate(C'', z, C') → C'''
  15. Polygon(A''', B''', C''') → P''', c''', a''', b'''
  16. Mirror(A''', c''') → A''''
  17. Mirror(B''', c''') → B''''
  18. Mirror(C''', c''') → C''''
  19. Polygon(A'''', B'''', C'''') → P'''', c'''', a'''', b''''
  20. Rotate(A'''', z, B''') → A'''''
  21. Rotate(B'''', z, B''') → B'''''
  22. Rotate(C'''', z, B''') → C'''''
  23. Polygon(A''''', B''''', C''''') → P''''', c''''', a''''', b'''''
  24. Mirror(A''''', b''''') → A''''''
  25. Mirror(B''''', b''''') → B''''''
  26. Mirror(C''''', b''''') → C''''''
  27. Polygon(A'''''', B'''''', C'''''') → P'''''', c'''''', a'''''', b''''''
  28. Rotate(A'''''', z, C''''') → A'''''''
  29. Rotate(B'''''', z, C''''') → B'''''''
  30. Rotate(C'''''', z, C''''') → C'''''''
  31. Polygon(A''''''', B''''''', C''''''') → P''''''', c''''''', a''''''', b'''''''
  32. Mirror(A''''''', c''''''') → A''''''''
  33. Mirror(B''''''', c''''''') → B''''''''
  34. Mirror(C''''''', c''''''') → C''''''''
  35. Polygon(A'''''''', B'''''''', C'''''''') → P'''''''', c'''''''', a'''''''', b''''''''
  36. Rotate(A'''''''', z, B''''''') → A'''''''''
  37. Rotate(B'''''''', z, B''''''') → B'''''''''
  38. Rotate(C'''''''', z, B''''''') → C'''''''''
  39. Polygon(A''''''''', B''''''''', C''''''''') → P''''''''', c''''''''', a''''''''', b'''''''''
  40. Mirror(A''''''''', b''''''''') → A''''''''''
  41. Mirror(B''''''''', b''''''''') → B''''''''''
  42. Mirror(C''''''''', b''''''''') → C''''''''''
  43. Polygon(A'''''''''', B'''''''''', C'''''''''') → P'''''''''', c'''''''''', a'''''''''', b''''''''''
  44. Rotate(A'''''''''', z, C''''''''') → A'''''''''''
  45. Rotate(B'''''''''', z, C''''''''') → B'''''''''''
  46. Rotate(C'''''''''', z, C''''''''') → C'''''''''''
  47. Polygon(A''''''''''', B''''''''''', C''''''''''') → P''''''''''', c''''''''''', a''''''''''', b'''''''''''
  48. Mirror(A''''''''''', c''''''''''') → A''''''''''''
  49. Mirror(B''''''''''', c''''''''''') → B''''''''''''
  50. Mirror(C''''''''''', c''''''''''') → C''''''''''''
  51. Polygon(A'''''''''''', B'''''''''''', C'''''''''''') → P'''''''''''', c'''''''''''', a'''''''''''', b''''''''''''
  52. Rotate(A'''''''''''', z, B''''''''''') → A'''''''''''''
  53. Rotate(B'''''''''''', z, B''''''''''') → B'''''''''''''
  54. Rotate(C'''''''''''', z, B''''''''''') → C'''''''''''''
  55. Polygon(A''''''''''''', B''''''''''''', C''''''''''''') → P''''''''''''', c''''''''''''', a''''''''''''', b'''''''''''''
  56. Mirror(A''''''''''''', b''''''''''''') → A''''''''''''''
  57. Mirror(B''''''''''''', b''''''''''''') → B''''''''''''''
  58. Mirror(C''''''''''''', b''''''''''''') → C''''''''''''''
  59. Polygon(A'''''''''''''', B'''''''''''''', C'''''''''''''') → P'''''''''''''', c'''''''''''''', a'''''''''''''', b''''''''''''''
  60. Rotate(A'''''''''''''', z, C'''''''''''''') → A'''''''''''''''
  61. Rotate(B'''''''''''''', z, C'''''''''''''') → B'''''''''''''''
  62. Rotate(C'''''''''''''', z, C'''''''''''''') → C'''''''''''''''
  63. Polygon(A''''''''''''''', B''''''''''''''', C''''''''''''''') → P''''''''''''''', c''''''''''''''', a''''''''''''''', b'''''''''''''''

AI Drawing Prompt Reference

Draw an octagon by first creating a circle, then rotating points on the circle around the center to form a polygon, and further developing the shape through rotations and reflections to create a complex octagonal structure, finally calculating its area.
The prompt above was compiled from the original drawing commands and is for reference only.