平行四边形的面积公式

平行四边形的面积公式
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2024-02-06 18:07
本范例通过三个递进式开放问题引导学生探究平行四边形面积公式。①演示问题:给定底边a=6cm和对应高ha=2cm,计算平行四边形面积A=12cm²;②核心概念:利用「底×对应高」公式计算面积,理解不同边长与高度组合为何得到相同结果;③作图要点:使用Polygon绘制平行四边形,用Point和Segment确定顶点与边,用OrthogonalLine作高线,用Intersect求垂足,用Translate演示高平移后形成矩形的过程;④学段用途:适合5-6年级学生理解面积公式原理,培养几何直观与推理能力。

GeoGebra 命令及参数

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Textfield(input3) → InputBox3
  4. Textfield(input4) → InputBox4
  5. SpeechBubbleRight(E, 10, 2) → Vieleck1
  6. Polygon(F, H, G, I) → v1, f, g, h, i
  7. Spline({F, Midpoint[F, H], H}, 3) → AnimStrecke
  8. SelectedIndex(DD1) → index1
  9. SelectedIndex(DD2) → index2
  10. SelectedIndex(DD3) → index3
  11. Segment(TriAnimP2, TriAnimP3) → j
  12. Angle(TriAnimP3, TriAnimP2, TriAnimP1) → α
  13. Segment(TriAnimP3, TriAnimP1) → k
  14. Segment(TriAnimP2, TriAnimP1) → l
  15. SpeechBubbleRight(E, 9, 1.8) → Vieleck2
  16. Segment(I, J) → m
  17. Segment(J, H) → n
  18. Textfield(InputText) → InputBox5
  19. Polygon(I, J, F) → v2, p, q, r
  20. Polygon(TriAnimP1, TriAnimP2, TriAnimP3) → d1, trianimp3, trianimp1, trianimp2
  21. Polygon(I, J, H, G) → v3, i_2, j_1, h_2, g_2
  22. SelectedIndex(DD4) → index4
  23. SelectedIndex(DD5) → index5
  24. Segment(G, H) → Slide2
  25. Point(Slide2) → DynP2
  26. OrthogonalLine(DynP2, g) → s
  27. Intersect(s, Segment[F, I]) → O
  28. Point(Segment[DynP2, Anim2EndP], schieb3) → P
  29. Polygon(P, P + Vector[DynP2, O], P + Vector[DynP2, F], P + Vector[DynP2, H]) → v4, p_1, t, a, b
  30. Polygon(DynP2, O, I, G) → v5, dynp2, o, i_1, g_1
  31. SpeechBubbleRight(POSSpeechStep6, 10, 1.6) → SpeechStep6
  32. Angle(P + Vector[DynP2, F], P + Vector[DynP2, O], P) → β
  33. Text("$\textsf{\textcolor{db6114}{\bold{h_b}}}$", Midpoint[P, P + Vector[DynP2, O]] - (0.5 * UnitOrthogonalVector[Segment[DynP2, O]]), false, true, 0, 0) → Text4
  34. SpeechBubbleRight(R, 11.5, 2) → SpeechBubbleStep7
  35. Translate(v4, Vector[F, POSVEnd2]) → v4'
  36. Translate(DynP2, Vector[F, POSVEnd2]) → DynP2'
  37. Translate(O, Vector[F, POSVEnd2]) → O'
  38. Translate(I, Vector[F, POSVEnd2]) → I'
  39. Translate(G, Vector[F, POSVEnd2]) → G'
  40. Polygon(DynP2', O', I', G') → v5', dynp2', o', i', g'
  41. Translate(TriAnimP1, Vector[F, POSVEnd1]) → TriAnimP1'
  42. Translate(TriAnimP2, Vector[F, POSVEnd1]) → TriAnimP2'
  43. Translate(TriAnimP3, Vector[F, POSVEnd1]) → TriAnimP3'
  44. Polygon(TriAnimP1', TriAnimP2', TriAnimP3') → d1', trianimp3', trianimp1', trianimp2'
  45. Translate(I, Vector[F, POSVEnd1]) → I'_{1}
  46. Translate(J, Vector[F, POSVEnd1]) → J'
  47. Translate(H, Vector[F, POSVEnd1]) → H'
  48. Translate(G, Vector[F, POSVEnd1]) → G'_{1}
  49. Polygon(I'_{1}, J', H', G'_{1}) → v3', i'_{1}, j', h', g'_{1}
  50. Angle(Translate[P + Vector[DynP2, F], Vector[F, POSVEnd2]], Translate[P + Vector[DynP2, O], Vector[F, POSVEnd2]], Translate[P, Vector[F, POSVEnd2]]) → γ
  51. Angle(TriAnimP3', TriAnimP2', TriAnimP1') → δ
  52. PolyLine(G'_{1}, H', J', I'_{1}, G'_{1}) → VEndPoly1
  53. PolyLine(TriAnimP3', TriAnimP2', TriAnimP1', TriAnimP3') → VEndPoly2
  54. Translate(a, Vector[F, POSVEnd2]) → a'
  55. Translate(b, Vector[F, POSVEnd2]) → b'
  56. Translate(p_1, Vector[F, POSVEnd2]) → c
  57. Translate(t, Vector[F, POSVEnd2]) → t'
  58. Segment(DynP2, P) → d
  59. Translate(F, Vector[F, EndSkizz3POS]) → EndSkizz3P1
  60. Translate(H, Vector[F, EndSkizz3POS]) → EndSkizz3P2
  61. Translate(G, Vector[F, EndSkizz3POS]) → EndSkizz3P3
  62. Translate(I, Vector[F, EndSkizz3POS]) → EndSkizz3P4
  63. Midpoint(EndSkizz3P1, EndSkizz3P3) → EndSkizz3M
  64. PolyLine({EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P1] * relsizeEndSkizz), EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P2] * relsizeEndSkizz), EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P3] * relsizeEndSkizz), EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P4] * relsizeEndSkizz), EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P1] * relsizeEndSkizz)}) → EndSkizz3Outline
  65. Point(EndSkizz3Outline) → T
  66. Point(EndSkizz3Outline) → U
  67. Point(EndSkizz3Outline) → V
  68. Point(EndSkizz3Outline) → W
  69. Segment(W, V) → e
  70. Intersect(OrthogonalLine[U, e], e) → Z
  71. Point(EndSkizz3Outline) → A_1
  72. Intersect(OrthogonalLine[T, Segment[A_1, W]], Segment[A_1, W]) → B_1
  73. Segment(B_1, T) → radcon_1
  74. Segment(Z, U) → radcon_2
  75. Translate(TriAnimP2, Vector[F, POSVEnd1]) → TriAnimP2'_{1}
  76. Translate(TriAnimP3, Vector[F, POSVEnd1]) → TriAnimP3'_{1}
  77. Segment(TriAnimP2'_{1}, TriAnimP3'_{1}) → j'_{1}
  78. Translate(p_1, Vector[F, POSVEnd2]) → f_1

AI 绘图提示语参考

绘制一个平行四边形,给定底边a=6cm和高ha=2cm,计算面积A=12cm²。使用多边形工具绘制平行四边形,通过点和线段定义顶点和边,用垂直线定义高,通过交点确定垂足。将平行四边形通过平移变换为矩形,展示不同边和高的组合可以得到相同的面积。
以上提示语为根据原始绘图命令整理而来,仅供参考。