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梯形面积计算

梯形面积计算
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2023-12-05 23:33
多边形几何作图滑块动画
所属专题 Trapez - Flächeninhalt
①本范例演示梯形面积的计算方法；②涉及核心数学概念：梯形面积公式、公式应用与推导；③构造要点：使用了Polygon（多边形）、Centroid（重心）、Vector（向量）、Segment（线段）、Angle（角度）等GeoGebra命令/对象；④适合小学5-6年级学生，用于学习和练习梯形面积公式的应用与理解。

GeoGebra 命令及参数

  1. Polygon(A0, A1, A3, A2) → t1, a0, a1, a3, a2
  2. Centroid(t1) → AM
  3. Vector(AM, A0) → v0M
  4. SelectedIndex(DropDown6) → input6
  5. SelectedIndex(DropDown5) → input5
  6. SelectedIndex(DropDown4) → input4
  7. SelectedIndex(DropDown3) → input3
  8. SelectedIndex(DropDown2) → input2
  9. Point(Line[S1 + 0.6, yAxis]) → S2
  10. Point(Line[S2, yAxis]) → S3_{9}
  11. Point(Line[S2, yAxis]) → S3_{8}
  12. Point(Line[S2, yAxis]) → S3_{7}
  13. Point(Line[S2, yAxis]) → S3_{6}
  14. Point(Line[S2, yAxis]) → S3_{5}
  15. Point(Line[S2, yAxis]) → S3_{4}
  16. Point(Line[S2, yAxis]) → S3_{3}
  17. Point(Line[S2, yAxis]) → S3_{2}
  18. Point(Line[S2, yAxis]) → S3_{1}
  19. Element({1, 2, 3, 4, 5, 5.5, 6, 7, 8, 9, 10, 11}, step2) → step
  20. If(step ≟ 5.5, (13.77887, 0.065), (14.08785, 0.70358)) → S5_{6}
  21. Element({S5_{1}, S5_{2}, S5_{3}, S5_{4}, S5_{5}, S5_{6}, S5_{7}, S5_{8}, S5_{9}, S5_{9}}, step) → S5
  22. Textfield(input1) → Eingabefeld1
  23. Textfield(input2) → Eingabefeld2
  24. Segment(A2, Intersect[Line[A2, yAxis], a0]) → hTrapez
  25. Polygon(C0, C1, C3, C2) → t2, f, g, i, n
  26. Point(Line[F1, xAxis]) → F2
  27. Element({S3_{1}, S3_{2}, S3_{3}, S3_{4}, S3_{5}, S3_{6}, S3_{7}, S3_{8}, S3_{9}, S3_{9}}, step) → S3
  28. Mirror(S2, Line[S1, xAxis]) → S7
  29. Point(Line[FL1, xAxis]) → FL2
  30. Point(Line[FL3, xAxis]) → FL4
  31. If(choice ≟ 1, {B1, B3, A1, A3}, If[choice ≟ 2, {A2, A0, B2, B0}, {A0, A1, A3, A2}]) → listBlack
  32. Polygon(listBlack) → black
  33. Segment(listBlack(2), listBlack(3)) → a
  34. Segment(A2, Intersect[Line[A2, yAxis], a0]) → h
  35. Textfield(input7) → Eingabefeld7
  36. Polygon(A0, A1, A3, A2) → t3, j, k, l, m
  37. Point(Line[A, xAxis]) → B
  38. Angle(A2, Intersect[Line[A2, yAxis], Line[A0, xAxis]], A0) → α
  39. Point(Line[F3, xAxis]) → F4
  40. LaTeX(step, true, true) → Text18
  41. Element({M1, M2, M3, M4}, Mod[turncount, 4] + 1) → Mpos
  42. Point(Circle[CM, Length[v0M]]) → CD0
  43. Vector(AM, A3) → v3M
  44. Vector(AM, A1) → v1M
  45. Vector(AM, A2) → v2M
  46. Angle(A0, AM, A1) → winkel01
  47. Angle(A1, AM, A3) → winkel13
  48. Angle(A3, AM, A2) → winkel32
  49. Angle(A2, AM, A0) → winkel20
  50. Vector(CM, CD0) → vD
  51. Centroid(Polygon[C1, C3, C2, C0]) → CDM
  52. Length(v0M) → arrowCircleRadius
  53. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle))) + (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle)))]])) → arrowCircleArrow01
  54. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle))) - (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle)))]])) → arrowCircleArrow02

AI 绘图提示语参考

在坐标系中先给出一个梯形的四个顶点，按顺序连接形成梯形边形。计算并标出该梯形的重心点，从重心作指向某一顶点的向量以确定后续辅助方向。再在竖直坐标轴上取与两条水平基边对应的投影点，画出与梯形高相关的竖直线段，用作梯形高的度量。最后在图中标注从重心到相邻边方向的三个夹角，包含以顶点方向与边界射线形成的角，并在合适位置放置文本输入框用于选择参数与显示面积计算相关表达式。
以上提示语为根据原始绘图命令整理而来，仅供参考。