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梯形面积计算 by RV'SMath (2)

梯形面积计算 by RV'SMath (2)
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2016-01-31 13:09
多边形函数解析几何几何作图
所属专题 Complex Math
这个范例演示了如何通过 GeoGebra 计算梯形的面积。涉及的核心数学概念包括梯形面积公式、几何作图和解析几何。作图要点包括使用向量、点、线段、正交线、多边形、旋转、角度、镜像、交点等 GeoGebra 命令和对象来构建梯形并计算其面积。适合初中及以上学生学习和理解几何图形的性质。

GeoGebra 命令及参数

  1. Vector((0, 0), (0, b / 5)) → u
  2. Vector((b, 0), (b, b / c)) → v
  3. Point(u) → A
  4. Point(v) → B
  5. Segment(A, B) → d
  6. Point(u) → C
  7. Point(v) → D
  8. Segment(C, D) → e
  9. OrthogonalLine(E, e) → f
  10. Segment(E, F) → g
  11. Polygon(D, C, A, B) → poly1, d_1, c_1, a_1, b_1
  12. Vector((0, 0), (b, h)) → w
  13. Vector((b, 0), (b, h)) → i
  14. Vector((b, 0), (b, (2 * h))) → k
  15. Rotate(D, 10.45°, C) → D'
  16. Angle(D, C, D') → γ
  17. Segment(C, D') → l
  18. Point(l) → G
  19. Line(G, l) → m
  20. OrthogonalLine(B, e) → n
  21. Point(m) → I
  22. Segment(I, B) → p
  23. Point(i) → H
  24. Polygon(H, A, B) → poly2, b_2, h_1, a_2
  25. Polygon(H, A, I) → poly3, i_1, h_2, a_3
  26. Mirror(D, n) → D'_1
  27. Mirror(C, n) → C'
  28. Mirror(A, n) → A'
  29. Mirror(B, n) → B'
  30. Polygon(D'_1, C', A', B') → poly1', d'_1, c', a', b'
  31. Mirror(D'_1, c') → J
  32. Mirror(C', c') → C''
  33. Mirror(A', c') → A''
  34. Mirror(B', c') → B''
  35. Polygon(J, C'', A'', B'') → poly1'', j_1, c'', a'', b''
  36. Mirror(J, b'') → J'
  37. Mirror(C'', b'') → C'''
  38. Mirror(A'', b'') → A'''
  39. Mirror(B'', b'') → B'''
  40. Vector((0, 0), (0, (3 * b / 5))) → q
  41. Point(q) → K
  42. Segment(K, B''') → r
  43. Point(d) → L
  44. Intersect(c', a') → M
  45. Polygon(B', L, K, B'', M) → poly4, b'_1, l_1, k_1, b''_1, m_1
  46. Intersect(r, l_1) → O
  47. Textfield(a) → InputBox1
  48. Segment(C, O) → t