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Trapezium Area Calculation by Liam Fielder

Trapezium Area Calculation by Liam Fielder
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2017-03-24 18:40
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to dynamically calculate the area of a trapezium using GeoGebra. It involves core mathematical concepts such as the definition of a trapezium, area formula, and coordinate geometry. Key construction steps include using commands like Segment, Line, Point, Polygon, OrthogonalLine, Intersect, Vector, Translate, Midpoint, Angle, and PointIn to build the trapezium and auxiliary lines, followed by calculating base lengths and heights to derive the area. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Line(C, f) → g
  3. Segment(A, C) → h_1
  4. Point(g) → D
  5. Segment(B, D) → i
  6. Polygon(A, C, D, B) → poly1, c, a, d, b
  7. Point(f) → E
  8. OrthogonalLine(E, a) → h_2
  9. Intersect(h_2, a) → F
  10. Segment(E, F) → h
  11. Vector(I, J) → v
  12. Vector(G, H) → u
  13. Translate(A, u) → A'
  14. Translate(C, u) → C'
  15. Translate(D, u) → D'
  16. Translate(B, u) → B'
  17. Translate(A', v) → A''
  18. Translate(C', v) → C''
  19. Translate(D', v) → D''
  20. Translate(B', v) → B''
  21. Translate(A, v) → A'_1
  22. Translate(C, v) → C'_1
  23. Translate(D, v) → D'_1
  24. Translate(B, v) → B'_1
  25. Polygon(C', D', B') → poly3, b'_3, c'_3, d'_2
  26. Midpoint(D', B') → K
  27. Midpoint(A'', C'') → L
  28. Midpoint(B'', D'') → M
  29. Polygon(L, C'', D'', M) → poly5, l_1, c''_2, d''_2, m_1
  30. Midpoint(A'_1, C'_1) → N
  31. Midpoint(D'_1, B'_1) → O
  32. Angle(F, E, A) → α
  33. Translate(A'', v) → A'''
  34. Translate(C'', v) → C'''_1
  35. Translate(D'', v) → D'''_1
  36. Translate(B'', v) → B'''
  37. PointIn(poly1) → Pointpoly1