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梯形面积计算 by Toby Jacobson

梯形面积计算 by Toby Jacobson
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2017-01-18 09:55
多边形三角函数几何作图
①本范例演示了如何通过构造等腰三角形和辅助线段来计算梯形面积；②涉及的核心数学概念包括梯形、等腰三角形、几何作图、对数函数；③作图要点——从下方『构造摘要』提炼用到了Line, Point, Segment, OrthogonalLine, Intersect, Midpoint, Polygon, Rotate等GeoGebra命令/对象；④适合高中数学教学或几何作图爱好者学习使用。

GeoGebra 命令及参数

  1. Line(A, B) → f
  2. Line(C, f) → g
  3. Point(f) → D
  4. Point(f) → E
  5. Point(g) → F
  6. Point(g) → G
  7. Segment(D, F) → h
  8. Segment(E, G) → i
  9. OrthogonalLine(C, g) → j
  10. Intersect(f, j) → H
  11. Segment(C, H) → height
  12. Segment(F, G) → base1
  13. Segment(D, E) → base2
  14. Midpoint(h) → I
  15. Midpoint(i) → J
  16. OrthogonalLine(I, base2) → k
  17. OrthogonalLine(J, base2) → n
  18. Intersect(k, base2) → K
  19. Intersect(n, base2) → L
  20. Polygon(I, D, K) → poly1, k_1, i_1, d
  21. Polygon(J, L, E) → poly2, e, j_1, l_1
  22. Polygon(F, I, K, L, J, G) → poly3, f_1, i_2, k_2, l_2, j_2, g_1
  23. Rotate(I, (-α), I) → I'
  24. Rotate(D, (-α), I) → D'
  25. Rotate(K, (-α), I) → K'
  26. Polygon(I', D', K') → poly1', k', i', d'
  27. Rotate(J, α, J) → J'
  28. Rotate(L, α, J) → L'
  29. Rotate(E, α, J) → E'
  30. Polygon(J', L', E') → poly2', e', j', l'