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Calculating Area of Parallelogram by Ooi Soo Huat

Calculating Area of Parallelogram by Ooi Soo Huat
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2017-12-11 14:36
VectorCoordinate GeometryGeometric Construction
In collections Mathematics Form 1
This example demonstrates how to calculate the area of a parallelogram using vector methods. Key math concepts include vectors, cross product, and geometric construction. It utilizes commands like Line, Point, Vector, and Polygon to draw the parallelogram and compute the magnitude of the cross product of vectors. Suitable for high school students and beginners needing to understand vector applications.

GeoGebra Commands & Parameters

  1. Line(A, yAxis) → b
  2. Line(A, xAxis) → a
  3. Point(a) → B
  4. Distance(A, B) → AB
  5. Line(B, b) → c
  6. Point(c) → C
  7. Line(C, a) → d
  8. Point(d) → G
  9. Intersect(b, d) → D
  10. If(NearC ≟ true, C, G) → Pm
  11. DynamicCoordinates(G, x(Pm), y(Pm)) → E
  12. Line(E, c) → g
  13. Intersect(a, g) → H
  14. Circle(E, AB) → e
  15. Intersect(e, d, 1) → F
  16. Line(F, b) → h
  17. Intersect(a, h) → I
  18. Distance(C, E) → EC
  19. Distance(E, H) → EH
  20. If(E_B ≟ true, Polygon[E, B, H], Polygon[E, B, C]) → poly1
  21. Polygon(I, B, C, F) → poly2, i, b_2, c_2, f
  22. If(E_B ≟ true, Polygon[F, A, D], Polygon[F, A, I]) → poly3
  23. Polygon(A, H, E, D) → poly4, a_1, h_1, e_1, d_1
  24. Polygon(A, B, C, D) → poly5, a_2, b_1, c_1, d_2
  25. Vector(C, D) → u
  26. If(E_R ≟ true, Translate[poly1, Vector[(m * u)]], Translate[poly3, Vector[(m * (-u))]]) → Trans
  27. Midpoint(D, A) → J
  28. Line(J, a) → j
  29. Circle(J, n) → k
  30. Intersect(k, j, 1) → K
  31. Line(K, h) → l
  32. Circle(K, n) → p
  33. Intersect(p, l, 2) → L
  34. Intersect(p, l, 1) → M
  35. Intersect(d, l) → N
  36. Intersect(a, l) → O
  37. Vector(M, O) → v
  38. Vector(L, N) → w
  39. Midpoint(A, B) → P
  40. Circle(P, n) → q
  41. Line(P, c) → r
  42. Intersect(q, r, 1) → Q
  43. Line(Q, j) → s
  44. Circle(Q, n) → t
  45. Intersect(t, s, 1) → R
  46. Intersect(t, s, 2) → S
  47. Intersect(c, s) → T
  48. Intersect(b, s) → U
  49. Vector(R, U) → u_1
  50. Vector(S, T) → v_1
  51. Intersect(j, c) → V
  52. Circle(V, n) → f_1
  53. Intersect(f_1, c) → W, Z
  54. Segment(D, C) → k_1
  55. Segment(C, B) → l_1
  56. Segment(B, A) → m_1
  57. Intersect(f_1, j, 2) → A_1
  58. Line(A_1, r) → g_1
  59. Circle(A_1, n) → p_1
  60. Intersect(p_1, g_1, 2) → B_1
  61. Intersect(p_1, g_1, 1) → C_1
  62. Intersect(d, g_1) → D_1
  63. Intersect(a, g_1) → E_1
  64. Vector(B_1, D_1) → w_1
  65. Vector(C_1, E_1) → i_1
  66. Segment(A, D) → j_1
  67. Angle(A, D, C) → α
  68. Angle(C, B, A) → β
  69. SelectedIndex(Bahasa) → nn
  70. If(nn ≟ 1, "Derive the formula to calculate", "Menerbit rumus untuk menghitungkan") → Tex1
  71. If(nn ≟ 1, "the area of a parallelogram", "luas bentuk segi empat selari") → Tex2