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Measure 2D Shape Area

Measure 2D Shape Area
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2014-12-10 09:20
PolygonGeometric Construction
In collections P4 Area (I)
This example demonstrates how to measure the area of a 2D shape by counting the squares it covers. It involves core math concepts like area calculation and geometric intuition. GeoGebra commands and objects used include Segment, Vector, Point, Translate, and Polygon. Suitable for elementary and above, for geometric introduction and area concept teaching.

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) → 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