Triangle Area Calculation by Ooi Soo Huat

Triangle Area Calculation by Ooi Soo Huat
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2017-12-11 15:19
In collections Mathematics Form 1
This example demonstrates how to dynamically calculate the area of a triangle using GeoGebra. Key math concepts include coordinate geometry, vectors, polygon construction, and geometric drawing. The construction involves commands and objects like Line, Point, Intersect, Polygon, Vector, and Angle as per the summary. Suitable for high school mathematics teaching to understand the area formula and dynamic geometric properties.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → a
  2. Line(A, yAxis) → b
  3. Point(a) → B
  4. Line(B, b) → c
  5. Point(c) → C
  6. Line(C, a) → d
  7. Point(d) → G
  8. Intersect(b, d) → D
  9. If(NearC ≟ true, C, If[NearD ≟ true, D, G]) → Pm
  10. DynamicCoordinates(G, x(Pm), y(Pm)) → E
  11. Polygon(A, E, B) → poly1, b_1, a_1, e
  12. OrthogonalLine(E, d) → f
  13. Intersect(a, f) → F
  14. Polygon(E, D, A) → poly2, a_2, e_1, d_1
  15. Polygon(E, C, B) → poly3, b_2, e_2, c_1
  16. Polygon(B, F, E) → poly4, e_3, b_3, f_1
  17. Polygon(A, E, F) → poly5, f_2, a_3, e_4
  18. Midpoint(F, A) → H
  19. Midpoint(F, B) → I
  20. Midpoint(A, D) → J
  21. Midpoint(B, C) → K
  22. Midpoint(A, B) → L
  23. Midpoint(D, C) → M
  24. Circle(D, ja) → g
  25. Circle(A, ja) → h
  26. Circle(J, ja) → k
  27. Line(J, K) → i
  28. Intersect(g, d, 1) → N
  29. Circle(K, ja) → p
  30. Intersect(k, b, 2) → O
  31. Intersect(p, c, 2) → P
  32. Intersect(k, b, 1) → Q
  33. Intersect(p, c, 1) → R
  34. Line(O, P) → j
  35. Line(Q, R) → l
  36. Circle(O, ja) → q
  37. Circle(Q, ja) → s
  38. Intersect(q, j, 1) → S
  39. Intersect(s, l, 1) → T
  40. Vector(S, N) → u
  41. Intersect(h, a, 1) → U
  42. Vector(T, U) → v
  43. Circle(C, ja) → r
  44. Intersect(g, b, 2) → V
  45. Intersect(r, c, 2) → W
  46. Circle(M, ja) → t
  47. Intersect(t, d) → Z, A_1
  48. Circle(L, ja) → g_1
  49. Intersect(g_1, a) → B_1, C_1
  50. Line(C_1, A_1) → m
  51. Line(B_1, Z) → n
  52. Circle(A_1, ja) → h_1
  53. Circle(Z, ja) → k_1
  54. Intersect(h_1, m, 2) → D_1
  55. Intersect(k_1, n, 2) → E_1
  56. Vector(D_1, W) → w
  57. Vector(E_1, V) → u_1
  58. If(x(E) < x(D), "c", "d") → Td
  59. Circle(H, ja) → p_1
  60. Intersect(p_1, a) → F_1, G_1
  61. Line(G_1, f) → i_1
  62. Line(F_1, i_1) → j_1
  63. Circle(G_1, ja) → q_1
  64. Circle(F_1, ja) → r_1
  65. Intersect(q_1, i_1, 1) → H_1
  66. Intersect(r_1, j_1, 1) → I_1
  67. Circle(F, ja) → s_1
  68. Intersect(s_1, a) → J_1, K_1
  69. Intersect(h, b, 1) → L_1
  70. Circle(B, ja) → d_2
  71. Intersect(d_2, c, 1) → O_1
  72. Intersect(s_1, f, 1) → M_1
  73. Circle(I, ja) → t_1
  74. Intersect(t_1, a) → N_1, P_1
  75. Line(P_1, c) → l_1
  76. Line(N_1, c) → m_1
  77. Circle(N_1, ja) → c_2
  78. Circle(P_1, ja) → g_2
  79. Intersect(c_2, m_1, 1) → Q_1
  80. Intersect(g_2, l_1, 1) → R_1
  81. If(x(E) < x(C), Vector[Q_1, M_1], Vector[R_1, M_1]) → n_1
  82. If(x(E) < x(C), Vector[R_1, O_1], Vector[Q_1, O_1]) → u_2
  83. If(x(E) > x(D), Vector[H_1, M_1], Vector[I_1, M_1]) → w_1
  84. If(x(E) > x(D), Vector[I_1, L_1], Vector[H_1, L_1]) → v_1
  85. Circle(P, ja) → h_2
  86. Circle(R, ja) → k_2
  87. Intersect(h_2, j, 2) → S_1
  88. Intersect(k_2, l, 2) → T_1
  89. Intersect(r, d, 2) → U_1
  90. Intersect(d_2, a, 2) → V_1
  91. Vector(S_1, U_1) → v_2
  92. Vector(T_1, V_1) → w_2
  93. Angle(A, D, E) → α
  94. Angle(E, B, A) → β
  95. Angle(E, F, B) → γ
  96. Angle(E, C, B) → δ
  97. Angle(B, A, E) → ε
  98. Angle(C, B, A) → ζ
  99. Angle(A, F, E) → η
  100. Angle(A, D, C) → θ
  101. FractionText(0.5) → text7
  102. SelectedIndex(Bahasa) → nn
  103. If(nn ≟ 1, LaTeX["\text{Area of red region = }"], LaTeX["\text{Luas rantau merah = }"]) → Tex1

AI Drawing Prompt Reference

Draw a triangle with dynamic area calculation. Start by plotting the coordinate axes and determining the triangle's vertices, then connect them to form the triangle. Next, identify key points using intersections and vectors, and construct auxiliary shapes like perpendicular lines, circles, and quadrilaterals. Finally, illustrate the area calculation process, incorporating midpoints, vectors, and helper shapes.
The prompt above was compiled from the original drawing commands and is for reference only.