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Calculate Perimeter and Area

Calculate Perimeter and Area
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2017-01-09 03:51
TriangleGeometric Construction
This example demonstrates how to use GeoGebra to calculate and visualize the perimeter and area of a triangle. Key math concepts include perimeter, area, and geometric construction. It utilizes commands/objects like Random, OrthogonalLine, Intersect, Segment, Point. Suitable for middle school and above students to explore basic properties of geometric figures.

GeoGebra Commands & Parameters

  1. Random(1, 10) → Height
  2. Random(1, 10) → Base
  3. OrthogonalLine(B, xAxis) → a
  4. OrthogonalLine(A, yAxis) → b
  5. Intersect(a, b) → C
  6. Segment(B, C) → c
  7. Segment(C, A) → d
  8. OrthogonalLine(B, c) → e
  9. OrthogonalLine(A, d) → f
  10. Intersect(e, f) → D
  11. Segment(A, D) → g
  12. Segment(D, B) → h
  13. Point(xAxis) → E
  14. Point(xAxis) → F
  15. Point(xAxis) → G
  16. Point(xAxis) → H
  17. Point(xAxis) → I
  18. Point(xAxis) → J
  19. Point(xAxis) → K
  20. Point(xAxis) → L
  21. Point(xAxis) → M
  22. OrthogonalLine(E, xAxis) → i
  23. OrthogonalLine(F, xAxis) → j
  24. OrthogonalLine(G, xAxis) → k
  25. OrthogonalLine(H, xAxis) → l
  26. OrthogonalLine(I, xAxis) → m
  27. OrthogonalLine(J, xAxis) → n
  28. OrthogonalLine(K, xAxis) → p
  29. OrthogonalLine(L, xAxis) → q
  30. OrthogonalLine(M, xAxis) → r
  31. Intersect(i, d) → N
  32. Intersect(j, d) → O
  33. Intersect(k, d) → P
  34. Intersect(l, d) → Q
  35. Intersect(m, d) → R
  36. Intersect(n, d) → S
  37. Intersect(p, d) → T
  38. Intersect(q, d) → U
  39. Intersect(r, d) → V
  40. Intersect(r, h) → W
  41. Intersect(q, h) → Z
  42. Intersect(p, h) → A_1
  43. Intersect(n, h) → B_1
  44. Intersect(m, h) → C_1
  45. Intersect(l, h) → D_1
  46. Intersect(k, h) → E_1
  47. Intersect(j, h) → F_1
  48. Intersect(i, h) → G_1
  49. Segment(N, G_1) → s
  50. Segment(O, F_1) → t
  51. Segment(E_1, P) → a_1
  52. Segment(Q, D_1) → b_1
  53. Segment(C_1, R) → c_1
  54. Segment(S, B_1) → d_1
  55. Segment(A_1, T) → e_1
  56. Segment(U, Z) → f_1
  57. Segment(W, V) → g_1
  58. Point(yAxis) → H_1
  59. Point(yAxis) → I_1
  60. Point(yAxis) → J_1
  61. Point(yAxis) → K_1
  62. Point(yAxis) → L_1
  63. Point(yAxis) → M_1
  64. Point(yAxis) → N_1
  65. Point(yAxis) → O_1
  66. Point(yAxis) → P_1
  67. Point(yAxis) → Q_1
  68. OrthogonalLine(H_1, s) → h_1
  69. OrthogonalLine(I_1, s) → i_1
  70. OrthogonalLine(J_1, s) → j_1
  71. OrthogonalLine(K_1, s) → k_1
  72. OrthogonalLine(L_1, s) → l_1
  73. OrthogonalLine(M_1, s) → m_1
  74. OrthogonalLine(N_1, s) → n_1
  75. OrthogonalLine(O_1, s) → p_1
  76. OrthogonalLine(P_1, s) → q_1
  77. OrthogonalLine(Q_1, s) → r_1
  78. Intersect(r_1, g) → R_1
  79. Intersect(q_1, g) → S_1
  80. Intersect(p_1, g) → T_1
  81. Intersect(n_1, g) → U_1
  82. Intersect(m_1, g) → V_1
  83. Intersect(l_1, g) → W_1
  84. Intersect(k_1, g) → Z_1
  85. Intersect(j_1, g) → A_2
  86. Intersect(i_1, g) → B_2
  87. Intersect(h_1, g) → C_2
  88. Intersect(h_1, c) → D_2
  89. Intersect(i_1, c) → E_2
  90. Intersect(j_1, c) → F_2
  91. Intersect(k_1, c) → G_2
  92. Intersect(l_1, c) → H_2
  93. Intersect(m_1, c) → I_2
  94. Intersect(n_1, c) → J_2
  95. Intersect(p_1, c) → K_2
  96. Intersect(q_1, c) → L_2
  97. Intersect(r_1, c) → M_2
  98. Segment(C_2, D_2) → s_1
  99. Segment(E_2, B_2) → t_1
  100. Segment(A_2, F_2) → a_2
  101. Segment(G_2, Z_1) → b_2
  102. Segment(W_1, H_2) → c_2
  103. Segment(I_2, V_1) → d_2
  104. Segment(U_1, J_2) → e_2
  105. Segment(K_2, T_1) → f_2
  106. Segment(S_1, L_2) → g_2
  107. Segment(M_2, R_1) → h_2

AI Drawing Prompt Reference

Draw a right triangle with two randomly generated leg lengths. From the right-angle vertex, draw perpendiculars to the two coordinate axes, intersecting at a point to complete the triangle. Then from the other two vertices, draw perpendiculars to the opposite sides, intersecting at a point, and connect this point to the two vertices to form a rectangle. Place multiple random points on the base (x-axis), draw perpendiculars to the x-axis from each, and intersect these perpendiculars with the two slanted sides of the triangle, creating a series of intersection points that form a grid-like set of auxiliary lines inside and outside the triangle, illustrating the calculation of perimeter and area.
The prompt above was compiled from the original drawing commands and is for reference only.