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Trapezoid Area Calculation by Toby Jacobson

Trapezoid Area Calculation by Toby Jacobson
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2017-01-18 09:55
PolygonTrigonometryGeometric Construction
This example demonstrates how to calculate the area of a trapezoid by constructing isosceles triangles and auxiliary line segments. Key math concepts include trapezoids, isosceles triangles, geometric constructions, and logarithmic functions. It utilizes commands like Line, Point, Segment, OrthogonalLine, Intersect, Midpoint, Polygon, Rotate in GeoGebra. Suitable for high school mathematics teaching or for enthusiasts of geometric constructions.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(C, f) → g
  3. Point(f) → D
  4. Point(f) → E
  5. Point(g) → F
  6. Point(g) → G
  7. Segment(D, F) → h
  8. Segment(E, G) → i
  9. OrthogonalLine(C, g) → j
  10. Intersect(f, j) → H
  11. Segment(C, H) → height
  12. Segment(F, G) → base1
  13. Segment(D, E) → base2
  14. Midpoint(h) → I
  15. Midpoint(i) → J
  16. OrthogonalLine(I, base2) → k
  17. OrthogonalLine(J, base2) → n
  18. Intersect(k, base2) → K
  19. Intersect(n, base2) → L
  20. Polygon(I, D, K) → poly1, k_1, i_1, d
  21. Polygon(J, L, E) → poly2, e, j_1, l_1
  22. Polygon(F, I, K, L, J, G) → poly3, f_1, i_2, k_2, l_2, j_2, g_1
  23. Rotate(I, (-α), I) → I'
  24. Rotate(D, (-α), I) → D'
  25. Rotate(K, (-α), I) → K'
  26. Polygon(I', D', K') → poly1', k', i', d'
  27. Rotate(J, α, J) → J'
  28. Rotate(L, α, J) → L'
  29. Rotate(E, α, J) → E'
  30. Polygon(J', L', E') → poly2', e', j', l'