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Trapezoid Area Calculation

Trapezoid Area Calculation
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2023-12-05 23:33
PolygonGeometric ConstructionSlider Animation
In collections Trapez - Flächeninhalt
This example demonstrates the calculation methods for the area of a trapezoid. It involves core mathematical concepts such as the area formula for trapezoids, formula application, and derivation. GeoGebra commands/objects used in construction include Polygon, Centroid, Vector, Segment, and Angle. It is suitable for students in grades 5-6 to learn and practice the application and understanding of the trapezoid area formula.

GeoGebra Commands & Parameters

  1. Polygon(A0, A1, A3, A2) → t1, a0, a1, a3, a2
  2. Centroid(t1) → AM
  3. Vector(AM, A0) → v0M
  4. SelectedIndex(DropDown6) → input6
  5. SelectedIndex(DropDown5) → input5
  6. SelectedIndex(DropDown4) → input4
  7. SelectedIndex(DropDown3) → input3
  8. SelectedIndex(DropDown2) → input2
  9. Point(Line[S1 + 0.6, yAxis]) → S2
  10. Point(Line[S2, yAxis]) → S3_{9}
  11. Point(Line[S2, yAxis]) → S3_{8}
  12. Point(Line[S2, yAxis]) → S3_{7}
  13. Point(Line[S2, yAxis]) → S3_{6}
  14. Point(Line[S2, yAxis]) → S3_{5}
  15. Point(Line[S2, yAxis]) → S3_{4}
  16. Point(Line[S2, yAxis]) → S3_{3}
  17. Point(Line[S2, yAxis]) → S3_{2}
  18. Point(Line[S2, yAxis]) → S3_{1}
  19. Element({1, 2, 3, 4, 5, 5.5, 6, 7, 8, 9, 10, 11}, step2) → step
  20. If(step ≟ 5.5, (13.77887, 0.065), (14.08785, 0.70358)) → S5_{6}
  21. Element({S5_{1}, S5_{2}, S5_{3}, S5_{4}, S5_{5}, S5_{6}, S5_{7}, S5_{8}, S5_{9}, S5_{9}}, step) → S5
  22. Textfield(input1) → Eingabefeld1
  23. Textfield(input2) → Eingabefeld2
  24. Segment(A2, Intersect[Line[A2, yAxis], a0]) → hTrapez
  25. Polygon(C0, C1, C3, C2) → t2, f, g, i, n
  26. Point(Line[F1, xAxis]) → F2
  27. Element({S3_{1}, S3_{2}, S3_{3}, S3_{4}, S3_{5}, S3_{6}, S3_{7}, S3_{8}, S3_{9}, S3_{9}}, step) → S3
  28. Mirror(S2, Line[S1, xAxis]) → S7
  29. Point(Line[FL1, xAxis]) → FL2
  30. Point(Line[FL3, xAxis]) → FL4
  31. If(choice ≟ 1, {B1, B3, A1, A3}, If[choice ≟ 2, {A2, A0, B2, B0}, {A0, A1, A3, A2}]) → listBlack
  32. Polygon(listBlack) → black
  33. Segment(listBlack(2), listBlack(3)) → a
  34. Segment(A2, Intersect[Line[A2, yAxis], a0]) → h
  35. Textfield(input7) → Eingabefeld7
  36. Polygon(A0, A1, A3, A2) → t3, j, k, l, m
  37. Point(Line[A, xAxis]) → B
  38. Angle(A2, Intersect[Line[A2, yAxis], Line[A0, xAxis]], A0) → α
  39. Point(Line[F3, xAxis]) → F4
  40. LaTeX(step, true, true) → Text18
  41. Element({M1, M2, M3, M4}, Mod[turncount, 4] + 1) → Mpos
  42. Point(Circle[CM, Length[v0M]]) → CD0
  43. Vector(AM, A3) → v3M
  44. Vector(AM, A1) → v1M
  45. Vector(AM, A2) → v2M
  46. Angle(A0, AM, A1) → winkel01
  47. Angle(A1, AM, A3) → winkel13
  48. Angle(A3, AM, A2) → winkel32
  49. Angle(A2, AM, A0) → winkel20
  50. Vector(CM, CD0) → vD
  51. Centroid(Polygon[C1, C3, C2, C0]) → CDM
  52. Length(v0M) → arrowCircleRadius
  53. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle))) + (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle)))]])) → arrowCircleArrow01
  54. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle))) - (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle)))]])) → arrowCircleArrow02

AI Drawing Prompt Reference

Draw a coordinate-plane trapezoid by placing four vertices and connecting them in order to form the trapezoid shape. Mark the trapezoid’s centroid and draw an auxiliary vector from the centroid toward a chosen vertex to represent the key direction used for construction. On the vertical axis, create projection points that correspond to the trapezoid’s bases, and include a vertical segment representing the trapezoid height. Finally, annotate three angles determined by rays from the centroid toward the involved vertex directions, and provide text input fields to control selectable parameters and display the area-calculation expression.
The prompt above was compiled from the original drawing commands and is for reference only.