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梯形面积计算演示

梯形面积计算演示
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2016-06-22 02:58
解析几何最值优化
①本范例演示梯形面积的计算方法；②涉及核心数学概念包括梯形面积公式、旋转、线性规划、上和下和（黎曼和）、线性函数；③作图要点：使用Line, Ray, Point, Segment, Slope, PointIn, Midpoint, Dilate, Rotate, Polygon, OrthogonalLine, Intersect, Min, Circle等GeoGebra命令和对象；④适合高中数学教学，用于理解和应用梯形面积及相关优化问题。

GeoGebra 命令及参数

  1. Line(A, B) → f
  2. Ray(A, B) → g
  3. Point(g) → C
  4. Ray(A, C) → h
  5. Segment(A, C) → i
  6. Slope(i) → m
  7. PointIn(a) → D
  8. Line(D, i) → j
  9. Point(j) → E
  10. Ray(D, E) → k
  11. Point(k) → F
  12. Segment(D, F) → l
  13. Segment(A, D) → n
  14. Segment(F, C) → p
  15. Midpoint(p) → G
  16. Dilate(A, If[0 < c ≤ 1, 1 - c, 0], C) → A'
  17. Segment(A, A') → q
  18. Dilate(C, If[1 < c ≤ 2, 2 - c, 0], G) → C'
  19. Segment(C, C') → r
  20. Dilate(G, If[2 < c ≤ 3, 3 - c, 0], F) → G'
  21. Segment(G, G') → s
  22. Rotate(C, If[3 < c ≤ 4, ((c - 3) * π), π], G) → C'_1
  23. Rotate(C', If[3 < c ≤ 4, ((c - 3) * π), π], G) → C''
  24. Segment(C'_1, C'') → r'
  25. Dilate(F, If[4 < c ≤ 5, 5 - c, 0], D) → F'
  26. Segment(F, F') → t
  27. Dilate(D, If[5 < c ≤ 6, 6 - c, 0], A) → D'
  28. Segment(D, D') → d
  29. Dilate(D, If[6.5 < c ≤ 7.5, 7.5 - c, 0], G) → D'_1
  30. Polygon(A, C, G, D) → poly1, a_1, c_1, g_1, d_1
  31. Polygon(G, F, D) → poly2, d_2, g_2, f_1
  32. Segment(D, D'_1) → e
  33. Rotate(G, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → G'_1
  34. Rotate(F, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → F'_1
  35. Rotate(D, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → D'_2
  36. Polygon(G'_1, F'_1, D'_2) → poly2', d'_2, g'_1, f'_1
  37. Segment(F'_1, D'_2) → h_1
  38. Rotate(D, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → D'_3
  39. Rotate(D'_1, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → H
  40. Segment(D'_3, H) → e'
  41. Rotate(C'_1, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → I
  42. Rotate(C'', If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → C'''
  43. Segment(I, C''') → r''
  44. OrthogonalLine(D, q) → i_1
  45. Intersect(f, q) → J
  46. Dilate(D, If[6 < c ≤ 7, 7 - c, 0], J) → D'_4
  47. Segment(D, D'_4) → j_1
  48. Min(t, q) → o
  49. Circle(J, (0.15 * o)) → e_1
  50. Intersect(e_1, i_1) → K, L
  51. Intersect(e_1, f) → M, N
  52. Angle(D, J, A) → α
  53. Angle(C, A, D) → β
  54. Intersect(i_1, f) → O
  55. Dilate(D, If[6 < c ≤ 7, 7 - c, 0], O) → D'_5
  56. Segment(D, D'_5) → k_1
  57. Angle(A, O, D) → γ
  58. Point(f) → P
  59. Point(f) → Q
  60. Circle(C, t) → p_1
  61. Intersect(p_1, f, 2) → R
  62. Ray(R, Q) → m_1
  63. Angle(F, C, A) → δ