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菱形面积计算 by Ooi Soo Huat

菱形面积计算 by Ooi Soo Huat
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2017-12-11 15:35
多边形三角函数几何作图
①本范例演示如何通过构造菱形的对角线来计算其面积；②涉及的核心数学概念包括菱形的对角线性质、勾股定理、三角形面积公式；③作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象：SelectedIndex, Line, Point, Intersect, Segment, LineBisector, Midpoint, Circle, Angle, Polygon, Slope, If；④适合的学段或用途：高中数学几何教学，帮助学生理解菱形面积公式的推导过程。

GeoGebra 命令及参数

  1. SelectedIndex(Bahasa) → nn
  2. Line(A, xAxis) → a
  3. Line(A, yAxis) → b
  4. Point(a) → B
  5. Line(B, b) → c
  6. Point(c) → C
  7. Line(C, a) → d
  8. Intersect(b, d) → D
  9. Segment(D, C) → e
  10. Segment(C, B) → f
  11. Segment(B, A) → g
  12. Segment(A, D) → h
  13. Point(e) → E
  14. Line(E, h) → i
  15. Intersect(a, i) → F
  16. LineBisector(E, F) → j
  17. Intersect(b, j) → G
  18. Intersect(c, j) → H
  19. Midpoint(A, B) → I
  20. Circle(G, n) → q
  21. Intersect(q, j, 1) → J
  22. Line(J, i) → r
  23. Circle(J, n) → s
  24. Intersect(s, r, 2) → K
  25. Intersect(s, r, 1) → L
  26. Intersect(d, r) → M
  27. Intersect(a, r) → N
  28. Circle(I, n) → t
  29. Line(I, i) → a_1
  30. Intersect(t, a_1, 1) → O
  31. Line(O, j) → b_1
  32. Circle(O, n) → c_1
  33. Intersect(c_1, b_1, 2) → P
  34. Intersect(c_1, b_1, 1) → Q
  35. Intersect(b, b_1) → R
  36. Intersect(c, b_1) → S
  37. Segment(G, H) → d_1
  38. Segment(E, F) → e_1
  39. Intersect(d_1, e_1) → T
  40. Angle(E, T, G) → α
  41. Polygon(G, E, H, F) → poly1, g_1, e_2, h_1, f_1
  42. Polygon(D, G, E) → poly2, e_3, d_2, g_2
  43. Polygon(E, H, C) → poly3, c_2, e_4, h_2
  44. Polygon(F, B, H) → poly4, h_3, f_2, b_2
  45. Polygon(G, A, F) → poly5, f_3, g_3, a_2
  46. Angle(A, D, C) → β
  47. Angle(C, B, A) → γ
  48. Intersect(q, j, 2) → U
  49. Line(U, i) → k
  50. Intersect(a, k) → V
  51. Intersect(d, k) → W
  52. Line(A, C) → l
  53. Slope(l) → Arah
  54. Circle(U, n) → p
  55. Intersect(p, k, 1) → Z
  56. Intersect(p, k, 2) → A_1
  57. If(Arah > 0, Vector[K, M], Vector[A_1, W]) → u
  58. If(Arah > 0, Vector[L, N], Vector[Z, V]) → v
  59. If(Arah > 0, Vector[P, S], Vector[Q, S]) → u_1
  60. If(Arah > 0, Vector[Q, R], Vector[P, R]) → w
  61. If(nn ≟ 1, "Derive the formula to calculate", "Menerbit rumus untuk menghitungkan") → Tex1
  62. If(nn ≟ 1, "area of a kite based on area of triangles.", "luas bentuk lelayang berdasarkan luas segi tiga") → Tex2