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Measure 2D Shape Area by GeoGebra Institute of Hong Kong

Measure 2D Shape Area by GeoGebra Institute of Hong Kong
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2014-12-10 09:06
Coordinate GeometryGeometric 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, arithmetic mean, trapezoid, set theory, quadratic equations, and Pythagorean theorem. The construction uses commands like Segment, Vector, Translate, and Polygon, along with objects such as t2, t1, o1, o2, o, etc. It is suitable for middle school students and above, and for teaching purposes.

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. Segment((3, -1), (3, 3)) → l
  11. Translate(A, Vector[(t1 * Vector[A, D])]) → A'
  12. Translate(B, Vector[(t1 * Vector[A, D])]) → B'
  13. Translate(E, Vector[(t1 * Vector[A, D])]) → E'
  14. Polygon(A', B', E') → poly1, e', a', b'
  15. Translate(B, Vector[(t2 * Vector[B, A])]) → B'_1
  16. Translate(C, Vector[(t2 * Vector[B, A])]) → C'
  17. Translate(E, Vector[(t2 * Vector[B, A])]) → E'_1
  18. Polygon(B'_1, C', E'_1) → poly2, e'_1, b'_1, c'
  19. Translate(C, Vector[(t3 * Vector[D, A])]) → C'_1
  20. Translate(D, Vector[(t3 * Vector[D, A])]) → D'
  21. Translate(E, Vector[(t3 * Vector[D, A])]) → E'_2
  22. Polygon(C'_1, D', E'_2) → poly3, e'_2, c'_1, d'
  23. Translate(D, Vector[(t4 * Vector[A, B])]) → D'_1
  24. Translate(E, Vector[(t4 * Vector[A, B])]) → E'_3
  25. Translate(A, Vector[(t4 * Vector[A, B])]) → A'_1
  26. Polygon(D'_1, E'_3, A'_1) → poly4, a'_1, d'_1, e'_3
  27. Polygon(A', B', E') → poly1', e'_4, a'_2, b'_2
  28. Polygon(B'_1, C', E'_1) → poly2', e'_5, b'_3, c'_2
  29. Polygon(C'_1, D', E'_2) → poly3', e'_6, c'_3, d'_2
  30. Polygon(D'_1, E'_3, A'_1) → poly4', a'_3, d'_3, e'_7
  31. Polygon(A, B, C, D) → poly5, a, b, c, d
  32. Polygon(A, B, E) → poly6, e, a_1, b_1
  33. Polygon(B, C, E) → poly7, e_1, b_2, c_1
  34. Polygon(C, D, E) → poly8, e_2, c_2, d_1
  35. Polygon(A, D, E) → poly9, e_3, a_2, d_2