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Trapezoid Area Calculation Demo

Trapezoid Area Calculation Demo
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2016-06-22 02:58
Coordinate GeometryOptimization
This example demonstrates the calculation of a trapezoid's area, involving core math concepts like trapezoid area formula, rotation, linear programming, upper and lower sums (Riemann sums), and linear functions. It constructs the figure using commands such as Line, Ray, Point, Segment, Slope, PointIn, Midpoint, Dilate, Rotate, Polygon, OrthogonalLine, Intersect, Min, Circle, and objects like A, B, f, g, C, h, i, m, b, a, etc. Suitable for high school mathematics teaching, helping students understand and apply trapezoid area and related optimization problems.

GeoGebra Commands & Parameters

  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