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Interactive Discovery of Rhombus Area

Interactive Discovery of Rhombus Area
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2019-02-10 11:02
PolygonGeometric Construction
In collections Congruence (Vol 2) Area, Surface Area, Volume, Cross Section, 3D Perimeter & Area Perimeter & Area
This example demonstrates how to explore the calculation of rhombus area through interactive means, involving core math concepts like rhombus properties, area formulas, vector operations, and linear regression. Key GeoGebra commands and objects used include Rotate, Ray, Circle, Intersect, Polygon, Dilate, Segment, Vector, Translate, and CircleSector, making it suitable for high school mathematics instruction or student-led geometric property exploration.

GeoGebra Commands & Parameters

  1. Rotate(B, (a * π / 180), A) → B'
  2. Ray(A, B) → f
  3. Ray(A, B') → g
  4. Circle(B, Distance[A, B]) → c
  5. Circle(B', Distance[A, B]) → d
  6. Intersect(c, d, 2) → C
  7. Polygon(A, B, C, B') → q1, a_1, b, c_1, b'
  8. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], B) → A'
  9. Segment(A, A') → h
  10. Rotate(B, If[1 < e ≤ 2, ((a * (e - 1)) * π / 180), (a * π / 180)], A) → B'_1
  11. Segment(A, B'_1) → i
  12. Rotate(A, If[2 < e ≤ 3, (((180 - a) * (e - 2)) * π / 180), ((180 - a) * π / 180)], B'_1) → A'_1
  13. Segment(B'_1, A'_1) → j
  14. Dilate(A, If[3 < e ≤ 4, 4 - e, 0], B) → A'_2
  15. Vector(A, A'_2) → u
  16. Translate(A, u) → A'_3
  17. Translate(B'_1, u) → D
  18. Segment(A'_3, D) → i'
  19. Segment(B'_1, B) → k
  20. Segment(A, A'_1) → l
  21. Intersect(k, l) → E
  22. Polygon(B'_1, E, A) → t1, a_2, b'_1, e_1
  23. Polygon(A, E, B) → t2, b_1, a_3, e_2
  24. Polygon(B'_1, E, A'_1) → t3, a'_1, b'_2, e_3
  25. Polygon(B, A'_1, E) → t4, e_4, b_2, a'_2
  26. Dilate(A, If[5 < e ≤ 6, 6 - e, 0], E) → A'_4
  27. Segment(A, A'_4) → m
  28. Dilate(E, If[6 < e ≤ 7, 7 - e, 0], A'_1) → E'
  29. Segment(E, E') → n
  30. Rotate(A, If[7 < e ≤ 8, ((e - 7) * π), π], E) → A'_5
  31. Segment(E, A'_5) → p
  32. Dilate(B'_1, If[8 < e ≤ 9, 9 - e, 0], E) → F
  33. Segment(B'_1, F) → q
  34. Dilate(E, If[9 < e ≤ 10, 10 - e, 0], B) → E'_1
  35. Segment(E, E'_1) → r
  36. Rotate(B'_1, If[10 < e ≤ 11, ((e - 10) * π), π], E) → G
  37. Segment(E, G) → s
  38. Circle(E, (0.25 * Min[q, m])) → t
  39. Intersect(t, s, 1) → H
  40. Rotate(H, If[12 < e ≤ 13, ((e - 12) * π / 2), π / 2], E) → H'
  41. CircleSector(E, H, H') → d_1
  42. Rotate(d_1, If[14 < e ≤ 15, ((e - 14) * π / 2), π / 2], E) → f_1
  43. Dilate(A, If[16 < e ≤ 17, 17 - e, 0], B) → A'_6
  44. Vector(A, A'_6) → v
  45. Translate(B'_1, v) → I
  46. Translate(E, v) → E'_2
  47. Translate(A, v) → A'_7
  48. Polygon(I, E'_2, A'_7) → t1', a'_7, i_1, e'_2
  49. Translate(A, v) → A'_8
  50. Translate(B'_1, v) → J
  51. Segment(A'_8, J) → i'_1
  52. Translate(B'_1, v) → K
  53. Translate(F, v) → F'
  54. Segment(K, F') → q'
  55. Translate(A, v) → A'_9
  56. Translate(A'_4, v) → L
  57. Segment(A'_9, L) → m'
  58. Dilate(B'_1, If[17 < e ≤ 18, 18 - e, 0], A) → M
  59. Vector(B'_1, M) → w
  60. Translate(B'_1, w) → P
  61. Translate(E, w) → E'_3
  62. Translate(A'_1, w) → Q
  63. Polygon(P, E'_3, Q) → t3', q_1, p_1, e'_3
  64. Segment(M, Q) → g_1
  65. Translate(B'_1, w) → N
  66. Translate(F, w) → F'_1
  67. Segment(N, F'_1) → q'_1
  68. Translate(E, w) → E'_4
  69. Translate(A'_5, w) → O
  70. Segment(E'_4, O) → p'
  71. Segment(A, B'_1) → h_1
  72. Segment(B'_1, A'_1) → j_1
  73. Segment(E, B'_1) → k_1