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Animation to Show Trapezoid Area

Animation to Show Trapezoid Area
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2017-06-26 18:39
PolygonCoordinate GeometryCalculus
This example demonstrates the area calculation of a trapezoid through animation. It involves core math concepts like trapezoids, similar triangles, equations, definite integrals, linear regression, and bar charts. Constructed using GeoGebra commands such as Point, Sort, Element, DynamicCoordinates, Midpoint, If, Vector, Translate, Rotate, Semicircle, LaTeX, and Polygon. Suitable for high school mathematics education to visually explain the trapezoid area formula and integral applications.

GeoGebra Commands & Parameters

  1. Point(xAxis) → H
  2. Point(xAxis) → I
  3. Sort({H, I}) → list1
  4. Element(list1, 1) → A
  5. Element(list1, 2) → B
  6. DynamicCoordinates(K, Min[Max[x(K), x(A)], x(B)], y(K)) → L
  7. Midpoint(L, I) → D
  8. If(animate > 0.5, (2 * animate) - 1, 0) → animate2
  9. DynamicCoordinates(P, Min[Max[x(P), x(A)], x(B)], y(L)) → T
  10. Midpoint(T, H) → E
  11. Vector(E, (x(H), y(E))) → b
  12. Translate(E, Vector[(b * animate2)]) → E'_1
  13. Rotate(L, ((If[animate < 0.5, animate, 0.5] * 2) * π), D) → L'
  14. Rotate(D, ((If[animate < 0.5, animate, 0.5] * 2) * π), D) → D'_1
  15. Rotate(T, ((If[animate < 0.5, animate, 0.5] * 2) * π), D) → T'
  16. Rotate(E, ((If[animate < 0.5, animate, 0.5] * 2) * π), D) → E'
  17. Translate(E', Vector[(b * animate2)]) → E''
  18. Semicircle(C, B) → d
  19. Point(d, 1 - animate) → G
  20. Vector(H - (0, 1), I - (0, 1)) → u
  21. Vector(I - (0, 1), H - (0, 1)) → v
  22. Vector(J, M) → w
  23. Vector(M, J) → j
  24. Vector(N, J) → k
  25. Vector(J, N) → l
  26. LaTeX("\frac{h}{2}") → text3
  27. DynamicCoordinates(P, Min[Max[x(K), x(A)], x(B)], y(K)) → Q
  28. Polygon(D, E, T, L) → poly1, p, q, r, s
  29. Rotate(D, (animate * π), D) → D'
  30. Polygon(I, H, E'_1, D) → poly2, h, i, m, n
  31. Rotate(L, (animate * π), D) → K'
  32. Polygon(D'_1, E'', T', L') → poly1', t, c, e, f_1
  33. LaTeX("Area = \frac{h}{2}(a+b)") → text4
  34. Vector(E) → a
  35. If(animate < 0.5, animate, 0.5) → animate1
  36. Midpoint(L', T') → S
  37. Midpoint(T', H) → F
  38. Vector(H - (0, 1), T' - (0, 1)) → f
  39. Vector(T' - (0, 1), H - (0, 1)) → g