Rhombus Area Calculation and Geometric Construction

Rhombus Area Calculation and Geometric Construction
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2023-03-13 04:00
In collections geometriadinamica.es
This example demonstrates the calculation of the area of a rhombus, involving key mathematical concepts such as rhombus properties, area formulas, and geometric construction techniques. The construction involves GeoGebra commands like Circle, Ray, OrthogonalLine, etc. Suitable for middle school students learning geometry fundamentals or for mathematical teaching assistance.

GeoGebra Commands & Parameters

  1. Circle(A, D) → c
  2. Ray(A, B) → a
  3. Circle(A, d) → d_5
  4. OrthogonalLine(A, a) → b
  5. Intersect(d_5, b, 1) → C
  6. OrthogonalLine(C, b) → e
  7. Intersect(c, a, 1) → D_3
  8. OrthogonalLine(D_3, a) → f
  9. Intersect(f, e) → E
  10. Polygon(A, C, E, D_3) → P, a_1, c_1, e_1, d_1
  11. Circle(A, g) → h
  12. Intersect(h, a_1) → F,
  13. Intersect(h, d_1) → G,
  14. Mirror(A, G) → H
  15. Mirror(G, H) → I
  16. Mirror(H, I) → J
  17. Mirror(I, J) → K
  18. Mirror(J, K) → L
  19. Mirror(K, L) → M
  20. Mirror(L, M) → N
  21. Mirror(M, N) → O
  22. Mirror(N, O) → Q
  23. Mirror(O, Q) → R
  24. Mirror(Q, R) → S
  25. Mirror(R, S) → T
  26. Mirror(S, T) → U
  27. Mirror(A, F) → V
  28. Mirror(F, V) → W
  29. Mirror(V, W) → Y
  30. Mirror(W, Y) → Z
  31. Mirror(Y, Z) → A_1
  32. Mirror(Z, A_1) → B_1
  33. Mirror(A_1, B_1) → C_1
  34. Mirror(B_1, C_1) → D_1
  35. OrthogonalLine(G, d_1) → i
  36. OrthogonalLine(H, d_1) → j
  37. OrthogonalLine(I, d_1) → k
  38. OrthogonalLine(J, d_1) → l
  39. OrthogonalLine(K, d_1) → m
  40. OrthogonalLine(L, d_1) → n
  41. OrthogonalLine(M, d_1) → p
  42. OrthogonalLine(N, d_1) → q
  43. OrthogonalLine(O, d_1) → r
  44. OrthogonalLine(Q, d_1) → s
  45. OrthogonalLine(R, d_1) → t
  46. OrthogonalLine(S, d_1) → b_1
  47. OrthogonalLine(T, d_1) → f_1
  48. OrthogonalLine(U, d_1) → g_1
  49. OrthogonalLine(F, a_1) → h_1
  50. OrthogonalLine(V, a_1) → i_1
  51. OrthogonalLine(W, a_1) → j_1
  52. OrthogonalLine(Y, a_1) → k_1
  53. OrthogonalLine(Z, a_1) → l_1
  54. OrthogonalLine(A_1, a_1) → m_1
  55. OrthogonalLine(B_1, a_1) → n_1
  56. OrthogonalLine(C_1, a_1) → p_1
  57. OrthogonalLine(D_1, a_1) → q_1
  58. Intersect(c_1, i) → E_1
  59. Intersect(r, c_1) → F_1
  60. Segment(F_1, O) → r_1
  61. Intersect(j, c_1) → G_1
  62. Intersect(k, c_1) → H_1
  63. Intersect(l, c_1) → I_1
  64. Intersect(m, c_1) → J_1
  65. Intersect(n, c_1) → K_1
  66. Intersect(p, c_1) → L_1
  67. Intersect(q, c_1) → M_1
  68. Intersect(s, c_1) → N_1
  69. Intersect(t, c_1) → O_1
  70. Intersect(b_1, c_1) → P_1
  71. Intersect(f_1, c_1) → Q_1
  72. Intersect(g_1, c_1) → R_1
  73. Intersect(e_1, q_1) → S_1
  74. Intersect(e_1, p_1) → T_1
  75. Intersect(e_1, n_1) → U_1
  76. Intersect(m_1, e_1) → V_1
  77. Intersect(l_1, e_1) → W_1
  78. Intersect(k_1, e_1) → Y_1
  79. Intersect(j_1, e_1) → Z_1
  80. Intersect(i_1, e_1) → A_2
  81. Intersect(h_1, e_1) → B_2
  82. Segment(E_1, G) → s_1
  83. Segment(G_1, H) → t_1
  84. Segment(H_1, I) → a_2
  85. Segment(I_1, J) → b_2
  86. Segment(J_1, K) → c_2
  87. Segment(K_1, L) → d_2
  88. Segment(L_1, M) → e_2
  89. Segment(M_1, N) → f_2
  90. Segment(N_1, Q) → g_2
  91. Segment(O_1, R) → h_2
  92. Segment(P_1, S) → i_2
  93. Segment(Q_1, T) → j_2
  94. Segment(R_1, U) → k_2
  95. Segment(D_1, S_1) → l_2
  96. Segment(C_1, T_1) → m_2
  97. Segment(B_1, U_1) → n_2
  98. Segment(A_1, V_1) → p_2
  99. Segment(Z, W_1) → q_2
  100. Segment(Y, Y_1) → r_2
  101. Segment(W, Z_1) → s_2
  102. Segment(V, A_2) → t_2
  103. Segment(F, B_2) → a_3
  104. Circle(C_2, o) → c_3
  105. Point(c_3) → D_2
  106. Segment(C_2, D_2) → b_3
  107. Circle(D_2, C_2) → d_3
  108. OrthogonalLine(D_2, b_3) → e_3
  109. OrthogonalLine(C_2, b_3) → f_3
  110. Intersect(c_3, f_3, 2) → E_2
  111. Intersect(d_3, e_3, 2) → F_2
  112. Polygon(E_2, F_2, D_2, C_2) → P_2, e_4, f_4, d_4, c_4
  113. Midpoint(A, C) → G_2
  114. Midpoint(C, E) → H_2
  115. Midpoint(E, D_3) → I_2
  116. Midpoint(D_3, A) → J_2
  117. Polygon(G_2, H_2, I_2, J_2) → Q_2, g_3, h_3, i_3, j_3
  118. Segment(G_2, I_2) → k_3
  119. Segment(H_2, J_2) → l_3

AI Drawing Prompt Reference

Draw a rhombus by constructing two circles centered at one vertex, intersecting to determine the diagonals. Then, use perpendicular lines to find the other two vertices and connect them to form the rhombus. Next, draw an inscribed circle using the midpoint of one side, find intersections, and mirror the points to create a symmetric pattern around the rhombus.
The prompt above was compiled from the original drawing commands and is for reference only.