梯形面积变化的影响

梯形面积变化的影响
几何画板及绘图内容加载中,请稍等……
2023-12-05 23:33
本范例演示梯形面积在平行边长度和高度变化时的变化规律。核心数学概念包括梯形面积公式及其应用。通过GeoGebra命令如Polygon、Segment、Angle等进行几何作图。适合初中5-6年级学生学习和练习梯形面积计算与证明。

GeoGebra 命令及参数

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. SelectedIndex(dropDownH) → index2
  4. SelectedIndex(dropDownAC) → index1
  5. Sequence(Sequence[(IGotOptions(i) * IGotOptions(k)), i, 1, 4], k, 1, 4) → SolMatrix, {{0.25, 1, 0.125, 0.5}, {1, 4, 0.5, 2}, {0.125, 0.5, 0.0625, 0.25}, {0.5, 2, 0.25, 1}}
  6. Element(SolMatrix, matrixAC, matrixH) → matrixsol
  7. If(matrixsol ≟ 1 / 16, 2, matrixsol ≟ 2, 7, matrixsol ≟ 4, 8, matrixsol ≟ 1 / 8, 3, matrixsol ≟ 1 / 4, 4, matrixsol ≟ 1 / 2, 5, matrixsol ≟ 1, 6) → solindex
  8. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  9. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {8, 7, 0, 6, 7, 6, 5, 9, 5, 1, 2, 6, 9, 8, 0, 2, 9, 1, 6, 6, 5, 1, 3, 10, 10, 1, 0, 5, 3, 3, 7, 3, 1, 3, 5, 5, 0, 7, 0, 4, 9, 0, 5, 1, 7, 5, 4, 10, 0, 6, 8, 0, 3, 0, 1, 6, 4, 2, 3, 9, 0, 8, 10, 10, 5, 4, 1, 2, 3, 5, 7, 9, 0, 9, 8, 6, 9, 1, 4, 10, 1, 0, 6, 3, 6, 8, 3, 8, 10, 2, 9, 9, 7, 8, 7, 1, 0, 5, 0, 1}
  10. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  11. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 9, 5, 2, 3, 9, 5, 7, 1, 1, 3, 4, 9, 5, 4, 3, 7, 3, 0, 6, 9, 2, 1, 7, 10, 3, 3, 3, 0, 0, 0, 1, 6, 8, 10, 1, 1, 7, 0, 7, 0, 2, 5, 9, 5, 5, 6, 7, 4, 0, 10, 2, 6, 10, 3, 10, 0, 10, 9, 0, 7, 3, 8, 3, 0, 1, 0, 1, 5, 1, 7, 2, 2, 10, 1, 4, 10, 6, 4, 10, 3, 6, 8, 6, 6, 7, 9, 0, 3, 4, 3, 5, 3, 9, 3, 5, 4, 1, 0, 8}
  12. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  13. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  14. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  15. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  16. Remove(Sequence[If[stayY(i), randomNosForY(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. SelectedIndex(dropDownResult) → index4
  20. Polygon(A, B, C, D) → q1, a, b, c, d
  21. OrthogonalLine(C, a) → g
  22. Intersect(g, a) → E
  23. Segment(C, E) → h
  24. If(SelectedElement[dropDownH] ≟ dropDownH(1), lenH, SelectedElement[dropDownH] ≟ dropDownH(2), lenH / 2, SelectedElement[dropDownH] ≟ dropDownH(3), (lenH * 2), SelectedElement[dropDownH] ≟ dropDownH(4), lenH / 4, index2 ≟ 5, lenH) → lenHAdapted
  25. If(SelectedElement[dropDownAC] ≟ dropDownH(1), lenA, index1 ≟ 5, lenA, SelectedElement[dropDownAC] ≟ dropDownH(2), lenA / 2, SelectedElement[dropDownAC] ≟ dropDownH(3), (lenA * 2), SelectedElement[dropDownAC] ≟ dropDownH(4), lenA / 4, SelectedElement[dropDownAC] ≟ dropDownH(5), (lenA * 4)) → lenAAdapted
  26. If(SelectedElement[dropDownAC] ≟ dropDownH(1), lenC, index1 ≟ 5, lenC, SelectedElement[dropDownAC] ≟ dropDownH(2), lenC / 2, SelectedElement[dropDownAC] ≟ dropDownH(3), (lenC * 2), SelectedElement[dropDownAC] ≟ dropDownH(4), lenC / 4, SelectedElement[dropDownAC] ≟ dropDownH(5), (lenC * 4)) → lenCAdapted
  27. Polygon(A1, B1, C1, D1) → q2, a1, b1, c1, d1
  28. OrthogonalLine(C1, a1) → i
  29. Intersect(i, a1) → F
  30. Segment(C1, F) → h_1
  31. PolyLine(A, D, C, B) → Trapez1Zug
  32. Segment(A, D) → j
  33. Segment(CoordSystem2, CoordSystem3) → k
  34. Segment(CoordSystem2, CoordSystem1) → l
  35. Sequence(CoordSystem2 + ((i * 0.5), 0), i, 0, 28) → l1
  36. Sequence(Segment[l1(i), l1(i) + (0, 4.5)], i, 1, Length[l1]) → l2
  37. Sequence(CoordSystem2 + (0, (i * 0.5)), i, 0, 9) → l3
  38. Sequence(Segment[l3(i), l3(i) + (14, 0)], i, 1, Length[l3]) → l4
  39. Angle(C, E, A) → α
  40. Angle(C1, F, A1) → β
  41. SelectedIndex(DD) → index3
  42. Text("\textsf{||}", Midpoint[D, C] + (0, 0.05), false, true, 0, 0) → Text7
  43. Text("\textsf{||}", Midpoint[A, B] + (0, 0.05), false, true, 0, 0) → Text8
  44. Text("\textsf{||}", Midpoint[D1, C1] + (0, 0.05), false, true, 0, 0) → Text5
  45. Text("\textsf{||}", Midpoint[B1, A1] + (0, 0.05), false, true, 0, 0) → Text6
  46. Text(Text12, G, false, true, 0, 0) → Text14
  47. Text(Text13, H, false, true, 0, 0) → Text15
  48. Text(Text3, I, false, true, -1, 0) → Text17
  49. Text(Text4, J, false, true, 1, 0) → Text18

AI 绘图提示语参考

画一个梯形,展示其面积随平行边长度和高度变化的情况。梯形的两条平行边和高度可以调整,用不同颜色和标签标示出平行边和高度。在梯形下方绘制一个坐标系,并在坐标系中用不同颜色标示出梯形面积随平行边长度和高度变化的函数图像。在梯形旁边标注出平行边长度和高度的数值,并在坐标系中标注出函数图像的数值。
以上提示语为根据原始绘图命令整理而来,仅供参考。