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Area of a Trapezoid by RV'SMath

Area of a Trapezoid by RV'SMath
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2016-01-31 13:09
PolygonFunctionCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of a trapezoid using GeoGebra. The core mathematical concepts involved include the area formula for trapezoids, geometric constructions, and analytical geometry. Key construction points involve using GeoGebra commands and objects such as Vector, Point, Segment, OrthogonalLine, Polygon, Rotate, Angle, Line, Mirror, Intersect, and Textfield. Suitable for middle school and above students to learn and understand the properties of geometric shapes.

GeoGebra Commands & Parameters

  1. Vector((0, 0), (0, b / 5)) → u
  2. Vector((b, 0), (b, b / c)) → v
  3. Point(u) → A
  4. Point(v) → B
  5. Segment(A, B) → d
  6. Point(u) → C
  7. Point(v) → D
  8. Segment(C, D) → e
  9. OrthogonalLine(E, e) → f
  10. Segment(E, F) → g
  11. Polygon(D, C, A, B) → poly1, d_1, c_1, a_1, b_1
  12. Vector((0, 0), (b, h)) → w
  13. Vector((b, 0), (b, h)) → i
  14. Vector((b, 0), (b, (2 * h))) → k
  15. Rotate(D, 10.45°, C) → D'
  16. Angle(D, C, D') → γ
  17. Segment(C, D') → l
  18. Point(l) → G
  19. Line(G, l) → m
  20. OrthogonalLine(B, e) → n
  21. Point(m) → I
  22. Segment(I, B) → p
  23. Point(i) → H
  24. Polygon(H, A, B) → poly2, b_2, h_1, a_2
  25. Polygon(H, A, I) → poly3, i_1, h_2, a_3
  26. Mirror(D, n) → D'_1
  27. Mirror(C, n) → C'
  28. Mirror(A, n) → A'
  29. Mirror(B, n) → B'
  30. Polygon(D'_1, C', A', B') → poly1', d'_1, c', a', b'
  31. Mirror(D'_1, c') → J
  32. Mirror(C', c') → C''
  33. Mirror(A', c') → A''
  34. Mirror(B', c') → B''
  35. Polygon(J, C'', A'', B'') → poly1'', j_1, c'', a'', b''
  36. Mirror(J, b'') → J'
  37. Mirror(C'', b'') → C'''
  38. Mirror(A'', b'') → A'''
  39. Mirror(B'', b'') → B'''
  40. Vector((0, 0), (0, (3 * b / 5))) → q
  41. Point(q) → K
  42. Segment(K, B''') → r
  43. Point(d) → L
  44. Intersect(c', a') → M
  45. Polygon(B', L, K, B'', M) → poly4, b'_1, l_1, k_1, b''_1, m_1
  46. Intersect(r, l_1) → O
  47. Textfield(a) → InputBox1
  48. Segment(C, O) → t