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Area of Any Triangle

Area of Any Triangle
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2020-07-05 05:39
TriangleVectorGeometric Construction
This example demonstrates how to calculate the area of any triangle (obtuse or acute) using geometric transformations and constructions. Key mathematical concepts include geometric transformations, vectors, and the area formula for triangles. Using GeoGebra commands such as Line, Segment, OrthogonalLine, and Intersect, the construction of the triangle and area calculation are performed. Suitable for students in middle school and above learning geometric transformations and area calculations.

GeoGebra Commands & Parameters

  1. Line(A, B) → i
  2. Segment(A, B) → a
  3. Line(C, a) → b
  4. OrthogonalLine(C, b) → e
  5. OrthogonalLine(A, a) → c
  6. OrthogonalLine(B, a) → d
  7. Intersect(b, c) → D
  8. Intersect(d, b) → E
  9. Intersect(e, i) → F
  10. Mirror(F, C) → F'_1
  11. Polygon(F'_1, A, B) → poly1, b_1, f', a_1
  12. Intersect(b_1, b) → G
  13. Intersect(a_1, b) → H
  14. Polygon(D, G, A) → poly2, a_2, d_1, g
  15. Rotate(D, (-(Preuve°)), G) → D'
  16. Rotate(G, (-(Preuve°)), G) → G'
  17. Rotate(A, (-(Preuve°)), G) → A'_1
  18. Polygon(D', G', A'_1) → poly2', a', d', g'
  19. Polygon(H, E, B) → poly3, b_2, h, e_1
  20. Rotate(H, Preuve°, H) → H'
  21. Rotate(E, Preuve°, H) → E'
  22. Rotate(B, Preuve°, H) → B'_1
  23. Polygon(H', E', B'_1) → poly3', b', h', e'
  24. Polygon(G', H', B, A) → poly4, g'_1, h'_1, b_3, a_3
  25. Segment(C, F) → j
  26. Midpoint(I, J) → K
  27. Vector(K, I) → u
  28. Vector(K, J) → v
  29. Segment(A, I) → k
  30. Segment(B, J) → l
  31. Midpoint(j) → L
  32. Vector(A, M) → w
  33. Translate(F'_1, w) → F''_1
  34. Translate(A, w) → A'_2
  35. Translate(B, w) → B'_2
  36. Polygon(F''_1, A'_2, B'_2) → poly1', b'_1, f'', a'_1
  37. Translate(G', w) → G''_1
  38. Translate(H', w) → H''_1
  39. Segment(G''_1, H''_1) → m
  40. Translate(C, w) → C'
  41. Translate(F, w) → F'
  42. Segment(C', F') → j'
  43. Mirror(C', m) → C''
  44. Mirror(F', m) → F''
  45. Segment(C'', F'') → j''
  46. Polygon(F'', G''_1, H''_1) → poly5, h'', f''_1, g''
  47. Translate(G', w) → G''
  48. Translate(H', w) → H''
  49. Translate(B, w) → B'
  50. Translate(A, w) → A'
  51. Polygon(G'', H'', B', A') → poly4', g''_1, h''_1, b'_2, a'_2
  52. Segment(N, O) → n
  53. Segment(P, Q) → p
  54. Polygon(D, E, B, A) → q1, d_2, e_2, b_4, a_4
  55. Polygon(G, H, F'_1) → t1, f'_1, g_1, h_1
  56. Rotate(D, (-(Preuve°)), G) → D'_1
  57. Rotate(E, (-(Preuve°)), G) → E'_1
  58. Rotate(G, (-(Preuve°)), G) → G'_1
  59. Rotate(H, (-(Preuve°)), G) → H'_1
  60. Rotate(F'_1, (-(Preuve°)), G) → R
  61. Polygon(G'_1, H'_1, R) → t1', r, f, q
  62. Polygon(E, H, B) → t2, b_5, e_3, h_2
  63. Translate(E, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[E, D])]) → E'_2
  64. Translate(H, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[E, D])]) → H'_2
  65. Translate(B, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[E, D])]) → B'_3
  66. Polygon(E'_2, H'_2, B'_3) → t2', b'_3, e'_2, h'_2
  67. Polygon(G, E, B, A) → q2, g_2, e_4, b_6, a_5
  68. Segment(G, E) → s
  69. Segment(E, B) → t
  70. Segment(B, A) → f_1
  71. Segment(G, A) → i_1
  72. Intersect(a, b_1) → T
  73. Polygon(D, H, S, T) → q3, d_3, h_3, s_1, t_1
  74. Intersect(b_1, a_1) → U
  75. Intersect(d_3, h_3) → V
  76. Polygon(U, V, G) → t3, g_3, u_1, v_1
  77. Rotate(U, (-(Preuve°)), H) → U'
  78. Rotate(V, (-(Preuve°)), H) → V'
  79. Rotate(G, (-(Preuve°)), H) → G'_2
  80. Polygon(U', V', G'_2) → t3', g'_2, u', v'
  81. Polygon(G, D, A) → t4, a_6, g_4, d_4
  82. Translate(G, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[G'_1, G'_2])]) → G'_3
  83. Translate(D, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[G'_1, G'_2])]) → D'_2
  84. Translate(A, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[G'_1, G'_2])]) → A'_3
  85. Polygon(G'_3, D'_2, A'_3) → t4', a'_3, g'_3, d'_2
  86. Segment(D, E) → j_1
  87. Segment(E, B) → k_1
  88. Segment(D, A) → l_1
  89. Segment(D, G) → m_1
  90. Segment(D, A) → n_1
  91. Vector(C, C + (0.65, 0)) → w_1
  92. Vector(C, C - (0.65, 0)) → c_1
  93. Vector(C, C + (0, 0.65)) → p_1
  94. Vector(C, C - (0, 0.65)) → q_1
  95. Segment(M, F') → r_1
  96. Segment(A, F) → f_2