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Measuring Polygon Area

Measuring Polygon Area
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2019-04-02 01:19
PolygonVectorCoordinate GeometryGeometric Construction
This example demonstrates how to measure the area of any polygon using GeoGebra. Key math concepts include vectors, geometric transformations, polygon construction, and coordinate geometry. Construction highlights involve commands like Segment, Vector, Point, Rotate, Polygon, Max, Min, Translate. Suitable for high school mathematics, helping students understand area calculation methods and vector applications.

GeoGebra Commands & Parameters

  1. Segment(X0, X0 + (0, mark)) → h
  2. Segment(X0 + (1, 0), X0 + (1, mark)) → i
  3. Vector(X0 + (0, mark / 2), X0 + (1, mark / 2)) → u
  4. Vector(X0 + (1, mark / 2), X0 + (0, mark / 2)) → v
  5. Segment(Y0 - (mark, 0), Y0) → j
  6. Segment(Y0 - (mark, 1), Y0 - (0, 1)) → k
  7. Vector(Y0 - (mark / 2, 1), Y0 - (mark / 2, 0)) → w
  8. Vector(Y0 - (mark / 2, 0), Y0 - (mark / 2, 1)) → z
  9. Point(yAxis) → A
  10. Point(xAxis) → B
  11. Point(xAxis) → C
  12. Rotate(E, (90° * t1), F) → E'
  13. Rotate(F, (90° * t1), F) → F'
  14. Rotate(L, (90° * t1), F) → L'
  15. Polygon(E', F', L') → poly1, l', e', f'
  16. Rotate(G, ((-(90°)) * t2), F) → G'
  17. Rotate(M, ((-(90°)) * t2), F) → M'
  18. Rotate(F, ((-(90°)) * t2), F) → F'_1
  19. Polygon(G', M', F'_1) → poly2, f'_1, g', m'
  20. Rotate(D, ((-(180°)) * t3), J) → D'
  21. Rotate(E, ((-(180°)) * t3), J) → E'_1
  22. Rotate(J, ((-(180°)) * t3), J) → J'
  23. Polygon(D', E'_1, J') → poly3, j', d', e'_1
  24. Rotate(J, (180° * t4), J) → J'_1
  25. Rotate(K, (180° * t4), J) → K'
  26. Rotate(C, (180° * t4), J) → C'
  27. Polygon(J'_1, K', C') → poly4, c', j'_1, k'
  28. Max(t5 - 1, 0) → s2
  29. Min(t5, 1) → s1
  30. Min(t6, 1) → w1
  31. Max(t6 - 1, 0) → w2
  32. Translate(Translate[G, Vector[(s1 * Vector[M, H])]], Vector[(s2 * Vector[M, B])]) → G''
  33. Translate(Translate[M, Vector[(s1 * Vector[M, H])]], Vector[(s2 * Vector[M, B])]) → M''
  34. Translate(Translate[H, Vector[(s1 * Vector[H, M])]], Vector[(s2 * Vector[M, B])]) → H''
  35. Polygon(G'', H'', M'') → poly5, m'', g'', h''
  36. Translate(Translate[B, Vector[(w1 * Vector[N, A])]], Vector[(w2 * Vector[B, M])]) → B'
  37. Translate(Translate[N, Vector[(w1 * Vector[N, A])]], Vector[(w2 * Vector[B, M])]) → N'
  38. Translate(Translate[A, Vector[(w1 * Vector[A, N])]], Vector[(w2 * Vector[B, M])]) → A'
  39. Polygon(A', B', N') → poly6, n', a', b'
  40. Polygon(E', F', L') → poly1', l'_1, e'_2, f'_2
  41. Polygon(G', M', F'_1) → poly2', f'_3, g'_1, m'_1
  42. Polygon(D', E'_1, J') → poly3', j'_2, d'_1, e'_3
  43. Polygon(J'_1, K', C') → poly4', c'_1, j'_3, k'_1
  44. Polygon(G'', H'', M'') → poly5', m''_1, g''_1, h''_1
  45. Polygon(A', B', N') → poly6', n'_1, a'_1, b'_1
  46. Polygon(H, I, N, B, C, K, J, L) → poly7, h_1, i_1, n, b, c, k_1, j_1, l
  47. Polygon(A, B, C, D, E, F, G, H, I) → poly8, a, b_1, c_1, d, e, f, g, h_2, i_2
  48. Polygon(E, F, L) → poly9, l_1, e_1, f_1
  49. Polygon(F, G, M) → poly10, m, f_2, g_1
  50. Polygon(G, H, M) → poly11, m_1, g_2, h_3
  51. Polygon(A, B, N) → poly12, n_1, a_1, b_2
  52. Polygon(C, K, J) → poly13, j_2, c_2, k_2
  53. Polygon(D, E, J) → poly14, j_3, d_1, e_2