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Polygon Area Measurement

Polygon Area Measurement
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2019-04-02 01:14
CirclePolygonVectorCoordinate GeometryGeometric Construction
This example demonstrates how to dynamically construct and measure the area of a polygon. Key math concepts include polygons, incircles, vector operations, and coordinate geometry. GeoGebra commands/objects used in construction: Segment, Vector, Point, Min, Max, Translate, Polygon. Suitable for high school mathematics teaching to understand polygon area calculation methods and dynamic geometric properties.

GeoGebra Commands & Parameters

  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) → B
  11. Min(t1, 1) → s1
  12. Max(t1 - 1, 0) → s2
  13. Translate(Translate[A, Vector[(s1 * Vector[A, C])]], Vector[(s2 * Vector[B, C])]) → A'
  14. Translate(Translate[B, Vector[(s1 * Vector[C, A])]], Vector[(s2 * Vector[B, C])]) → B'
  15. Translate(Translate[C, Vector[(s1 * Vector[C, A])]], Vector[(s2 * Vector[B, C])]) → C'
  16. Polygon(A', B', C') → poly1, c', a', b'
  17. Min(t2, 1) → w1
  18. Max(t2 - 1, 0) → w2
  19. Translate(Translate[A, Vector[(w1 * Vector[A, C])]], Vector[(w2 * Vector[D, C])]) → A''
  20. Translate(Translate[D, Vector[(w1 * Vector[C, A])]], Vector[(w2 * Vector[D, C])]) → D''
  21. Translate(Translate[C, Vector[(w1 * Vector[C, A])]], Vector[(w2 * Vector[D, C])]) → C''
  22. Polygon(A'', D'', C'') → poly2, c'', a'', d''
  23. Polygon(A', B', C') → poly1', c'_1, a'_1, b'_1
  24. Polygon(A'', D'', C'') → poly2', c''_1, a''_1, d''_1
  25. Polygon((1, 0), (3, 0), (3, 2), (1, 2)) → poly3, a, b, c, d
  26. Polygon(A, B, (1, 2), (1, 0), (3, 0), (3, 2), D) → poly4, a_1, b_1, e, f, l, m, d_1
  27. Polygon(A, B, C) → poly5, c_1, a_2, b_2
  28. Polygon(A, C, D) → poly6, d_2, a_3, c_2
  29. Segment((-1, 5.944976963954309), (5, 5.944976963954309)) → n