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测量二维图形面积

测量二维图形面积
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2014-12-10 09:20
多边形几何作图
所属专题 P4 Area (I)
①本范例演示通过数方格测量二维图形面积的方法；②涉及核心数学概念为面积计算、几何直观；③构造摘要中用到了Segment（线段）、Vector（向量）、Point（点）、Translate（平移）、Polygon（多边形）等GeoGebra命令和对象；④适合小学及以上学段，用于几何启蒙和面积概念教学。

GeoGebra 命令及参数

  1. Segment(X0, X0 + (0, 0.25)) → g
  2. Segment(X0, X0 + (0, mark)) → h
  3. Segment(X0 + (1, 0), X0 + (1, mark)) → i
  4. Vector(X0 + (0, mark / 2), X0 + (1, mark / 2)) → u
  5. Vector(X0 + (1, mark / 2), X0 + (0, mark / 2)) → v
  6. Segment(Y0 - (mark, 0), Y0) → j
  7. Segment(Y0 - (mark, 1), Y0 - (0, 1)) → k
  8. Vector(Y0 - (mark / 2, 1), Y0 - (mark / 2, 0)) → w
  9. Vector(Y0 - (mark / 2, 0), Y0 - (mark / 2, 1)) → z
  10. Point(yAxis) → A
  11. Point(xAxis) → D
  12. Translate(A, Vector[(t1 * Vector[A, D])]) → A'
  13. Translate(F, Vector[(t1 * Vector[A, D])]) → F'
  14. Translate(B, Vector[(t1 * Vector[A, D])]) → B'
  15. Polygon(A', F', B') → poly1, b', a', f'
  16. Translate(C, Vector[(t2 * Vector[D, A])]) → C'
  17. Translate(D, Vector[(t2 * Vector[D, A])]) → D'
  18. Translate(H, Vector[(t2 * Vector[D, A])]) → H'
  19. Translate(E, Vector[(t2 * Vector[D, A])]) → E'
  20. Polygon(C', D', H') → poly2, a, b, c
  21. Translate(B, Vector[(t3 * Vector[B, A])]) → B'_1
  22. Translate(C, Vector[(t3 * Vector[B, A])]) → C'_1
  23. Translate(E, Vector[(t3 * Vector[B, A])]) → E'_1
  24. Polygon(B'_1, C'_1, E'_1) → poly3, e'_1, b'_1, c'_1
  25. Translate(A, Vector[(t4 * Vector[A, B])]) → A'_1
  26. Translate(G, Vector[(t4 * Vector[A, B])]) → G'
  27. Translate(D, Vector[(t4 * Vector[A, B])]) → D'_1
  28. Polygon(A'_1, G', D'_1) → poly4, d'_1, a'_1, g'
  29. Polygon(E, F, G, H) → poly5, e, f, g_1, h_1
  30. Polygon(A', F', B') → poly1', b'_2, a'_2, f'_1
  31. Polygon(C', D', H') → poly2', d, l, m
  32. Polygon(B'_1, C'_1, E'_1) → poly3', e'_2, b'_3, c'_2
  33. Polygon(A'_1, G', D'_1) → poly4', d'_2, a'_3, g'_1
  34. Polygon(A, B, C, D) → poly6, a_1, b_1, c_1, d_1
  35. Polygon(A, B, F) → poly7, f_1, a_2, b_2
  36. Polygon(B, C, E) → poly8, e_1, b_3, c_2
  37. Polygon(C, D, H) → poly9, h_2, c_3, d_2
  38. Polygon(A, G, D) → poly10, d_3, a_3, g_2