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Trapezoid Area Calculation by aolver

Trapezoid Area Calculation by aolver
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2017-11-28 09:27
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the calculation of a trapezoid's area. Key mathematical concepts include the properties and area formula of a trapezoid. Using GeoGebra commands such as Line, Point, Segment, and Polygon, the construction process of the trapezoid is dynamically shown. Suitable for middle school and above students to learn geometric construction and area calculation.

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