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Trapezoid Area Calculation by Jorge Cássio

Trapezoid Area Calculation by Jorge Cássio
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2020-02-25 21:43
PolygonTrigonometryGeometric Construction
This example demonstrates the calculation of a trapezoid's area. It involves core mathematical concepts such as the area formula for trapezoids, geometric construction, and polygon creation. Key GeoGebra commands used include Segment, Line, Point, Polygon, Intersect, Circle, Rotate, Midpoint, and OrthogonalLine to construct the trapezoid and auxiliary shapes. Suitable for middle school students and above learning geometric constructions and area calculations, or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → Base
  2. Line(C, Base) → b
  3. Point(b) → D
  4. Point(b) → E_1
  5. Polygon(A, D, E_1, B) → pol1, a_1, d, e, b_1
  6. Line(A, e) → f
  7. Intersect(b, f) → G
  8. Intersect(b, d) → H
  9. Circle(E_1, B) → q
  10. Line(B, E_1) → n
  11. Intersect(q, n, 2) → K
  12. Rotate(B, spin, E_1) → B'
  13. Intersect(Base, b_1) → N
  14. Midpoint(e) → F
  15. Polygon(D, F, E_1) → pol2, e_1, d_1, f_1
  16. Polygon(A, B, F, D) → pol3, a, b_2, f_2, d_2
  17. Segment(D, E_1) → base
  18. Segment(F, E_1) → g
  19. Segment(D, F) → h
  20. Polygon(F, E_1, D) → pol4, d_3, f_3, e_2
  21. Rotate(F, (-spin), F) → F'
  22. Rotate(E_1, (-spin), F) → E
  23. Rotate(D, (-spin), F) → D'
  24. Polygon(F', E, D') → pol4', d', f', e'_1
  25. Segment(F, B) → j
  26. OrthogonalLine(D, Base) → k
  27. Intersect(k, Base) → I
  28. Segment(D, I) → l
  29. Segment(D', E) → base_1