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梯形在网格中的面积

梯形在网格中的面积
几何画板及绘图内容加载中，请稍等……
2023-12-05 23:33
多边形解析几何几何作图
所属专题 Trapez - Flächeninhalt
本范例演示梯形在网格中的面积计算。核心数学概念包括梯形面积公式及其应用。通过使用GeoGebra命令如Shuffle、Element、Zip等，学生可以动态探索梯形的面积变化。适合5-6年级学生进行练习。

GeoGebra 命令及参数

  1. Shuffle(Sequence[Random[3, coordheight - 4], m, 1, 100]) → randomNosForH, {3, 5, 3, 5, 4, 3, 5, 3, 6, 6, 6, 6, 3, 4, 5, 6, 4, 5, 6, 6, 4, 3, 5, 6, 4, 3, 5, 4, 5, 6, 6, 3, 4, 3, 5, 4, 6, 3, 4, 4, 3, 5, 5, 5, 6, 5, 6, 6, 4, 5, 6, 3, 6, 6, 3, 3, 6, 3, 5, 6, 6, 5, 4, 6, 6, 5, 6, 3, 3, 6, 3, 6, 6, 6, 3, 5, 6, 5, 3, 5, 6, 6, 5, 3, 3, 3, 4, 4, 5, 3, 5, 4, 6, 5, 4, 3, 5, 5, 6, 3}
  2. Element(randomNosForH, Mod[questionCount, 100] + 1) → numH
  3. Shuffle(Sequence[Random[6, coordwidth - 2], m, 1, 100]) → randomNosForA, {9, 6, 7, 9, 7, 6, 10, 8, 9, 8, 9, 9, 10, 8, 9, 8, 8, 10, 7, 9, 9, 8, 8, 8, 9, 7, 8, 9, 6, 10, 9, 10, 9, 9, 6, 8, 9, 10, 6, 7, 6, 8, 8, 7, 9, 9, 9, 9, 6, 10, 9, 7, 10, 6, 6, 10, 10, 10, 10, 7, 7, 7, 10, 10, 6, 8, 10, 7, 9, 6, 9, 7, 8, 6, 7, 10, 8, 10, 10, 7, 8, 9, 7, 10, 9, 9, 9, 6, 6, 6, 7, 9, 9, 6, 8, 9, 6, 10, 8, 9}
  4. Element(randomNosForA, Mod[questionCount, 100] + 1) → numA
  5. Zip(Random[3, m - 1], m, randomNosForA) → randomNosForC
  6. Element(randomNosForC, Mod[questionCount, 100] + 1) → numC
  7. Zip(Max[{0, Random[1, coordwidth - a - 3]}], a, randomNosForC) → randomNosForAbsLinks
  8. Join(Sequence[Shuffle[{2, 3, 4, 5}], m, 1, 30]) → listEH
  9. Segment(PA, PC) → es
  10. Textfield(input1) → InputBox1
  11. Textfield(input2) → InputBox2
  12. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  13. Append(true, Sequence[If[randomNosForA(i) ≟ randomNosForA(i - 1), false, true], i, 2, 100]) → stayX
  14. Append(true, Sequence[If[randomNosForC(i) ≟ randomNosForC(i - 1), false, true], i, 2, 100]) → stayY
  15. Remove(Sequence[If[stayX(i), randomNosForA(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  16. Remove(Sequence[If[stayY(i), randomNosForC(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  17. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  18. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  19. Defined(input4) → fixed
  20. Flatten(Sequence[Sequence[O + (m * (size, 0)) + (j * (0, size)), m, 0, coordwidth - 1], j, 0, coordheight - 1]) → listPoints
  21. Random(2, numA - 2) → prop
  22. Segment(PB, PD) → fs
  23. Segment(G1, G2) → g
  24. Translate(Segment[(0, -0.1), (0, 0.1)], G1) → h
  25. Translate(Segment[(0, -0.1), (0, 0.1)], G2) → i
  26. Intersect(Line[PA, PB], Line[PD, yAxis]) → S
  27. Textfield(input4) → InputBox4
  28. Zip(Polygon[P, P + (0, size), P + (0, size) + (size, 0), P + (size, 0)], P, listPoints) → listCoords
  29. Segment(PD, Intersect[Line[PD, yAxis], Line[PA, xAxis]]) → f
  30. Angle(PB, S, PD) → α
  31. Textfield(input3) → InputBox3
  32. Segment(PA, PB) → streckea
  33. Segment(PD, PC) → streckec

AI 绘图提示语参考

在坐标网格中画一个梯形用于面积练习：给定两条平行的上、下边框，分别用四个顶点构成梯形的多边形。让顶点都落在网格交点附近，并设置上边与下边为左右相对的两条水平线段，左右两腰分别由上、下对应顶点连接形成。为辅助理解，画出梯形的一条腰的对应线段，以及与左右边的交点形成的角度标记；同时在图上放置若干输入框让用户记录高度与角度等参数，并可在网格中观察梯形形状变化。最后保证图形轮廓清晰可数。
以上提示语为根据原始绘图命令整理而来，仅供参考。