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Impact of Changes on Trapezoid Area

Impact of Changes on Trapezoid Area
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2023-12-05 23:33
PolygonCoordinate GeometryGeometric Construction
In collections Trapez - Flächeninhalt
This example demonstrates the changes in trapezoid area when the lengths of the parallel sides and height change. Key mathematical concepts include the trapezoid area formula and its application. It uses GeoGebra commands such as Polygon, Segment, and Angle for geometric construction. Suitable for 5-6th grade students to learn and practice trapezoid area calculation and proof.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. SelectedIndex(dropDownH) → index2
  4. SelectedIndex(dropDownAC) → index1
  5. Sequence(Sequence[(IGotOptions(i) * IGotOptions(k)), i, 1, 4], k, 1, 4) → SolMatrix, {{0.25, 1, 0.125, 0.5}, {1, 4, 0.5, 2}, {0.125, 0.5, 0.0625, 0.25}, {0.5, 2, 0.25, 1}}
  6. Element(SolMatrix, matrixAC, matrixH) → matrixsol
  7. If(matrixsol ≟ 1 / 16, 2, matrixsol ≟ 2, 7, matrixsol ≟ 4, 8, matrixsol ≟ 1 / 8, 3, matrixsol ≟ 1 / 4, 4, matrixsol ≟ 1 / 2, 5, matrixsol ≟ 1, 6) → solindex
  8. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  9. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {8, 7, 0, 6, 7, 6, 5, 9, 5, 1, 2, 6, 9, 8, 0, 2, 9, 1, 6, 6, 5, 1, 3, 10, 10, 1, 0, 5, 3, 3, 7, 3, 1, 3, 5, 5, 0, 7, 0, 4, 9, 0, 5, 1, 7, 5, 4, 10, 0, 6, 8, 0, 3, 0, 1, 6, 4, 2, 3, 9, 0, 8, 10, 10, 5, 4, 1, 2, 3, 5, 7, 9, 0, 9, 8, 6, 9, 1, 4, 10, 1, 0, 6, 3, 6, 8, 3, 8, 10, 2, 9, 9, 7, 8, 7, 1, 0, 5, 0, 1}
  10. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  11. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 9, 5, 2, 3, 9, 5, 7, 1, 1, 3, 4, 9, 5, 4, 3, 7, 3, 0, 6, 9, 2, 1, 7, 10, 3, 3, 3, 0, 0, 0, 1, 6, 8, 10, 1, 1, 7, 0, 7, 0, 2, 5, 9, 5, 5, 6, 7, 4, 0, 10, 2, 6, 10, 3, 10, 0, 10, 9, 0, 7, 3, 8, 3, 0, 1, 0, 1, 5, 1, 7, 2, 2, 10, 1, 4, 10, 6, 4, 10, 3, 6, 8, 6, 6, 7, 9, 0, 3, 4, 3, 5, 3, 9, 3, 5, 4, 1, 0, 8}
  12. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  13. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  14. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  15. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  16. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  17. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  18. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  19. SelectedIndex(dropDownResult) → index4
  20. Polygon(A, B, C, D) → q1, a, b, c, d
  21. OrthogonalLine(C, a) → g
  22. Intersect(g, a) → E
  23. Segment(C, E) → h
  24. If(SelectedElement[dropDownH] ≟ dropDownH(1), lenH, SelectedElement[dropDownH] ≟ dropDownH(2), lenH / 2, SelectedElement[dropDownH] ≟ dropDownH(3), (lenH * 2), SelectedElement[dropDownH] ≟ dropDownH(4), lenH / 4, index2 ≟ 5, lenH) → lenHAdapted
  25. If(SelectedElement[dropDownAC] ≟ dropDownH(1), lenA, index1 ≟ 5, lenA, SelectedElement[dropDownAC] ≟ dropDownH(2), lenA / 2, SelectedElement[dropDownAC] ≟ dropDownH(3), (lenA * 2), SelectedElement[dropDownAC] ≟ dropDownH(4), lenA / 4, SelectedElement[dropDownAC] ≟ dropDownH(5), (lenA * 4)) → lenAAdapted
  26. If(SelectedElement[dropDownAC] ≟ dropDownH(1), lenC, index1 ≟ 5, lenC, SelectedElement[dropDownAC] ≟ dropDownH(2), lenC / 2, SelectedElement[dropDownAC] ≟ dropDownH(3), (lenC * 2), SelectedElement[dropDownAC] ≟ dropDownH(4), lenC / 4, SelectedElement[dropDownAC] ≟ dropDownH(5), (lenC * 4)) → lenCAdapted
  27. Polygon(A1, B1, C1, D1) → q2, a1, b1, c1, d1
  28. OrthogonalLine(C1, a1) → i
  29. Intersect(i, a1) → F
  30. Segment(C1, F) → h_1
  31. PolyLine(A, D, C, B) → Trapez1Zug
  32. Segment(A, D) → j
  33. Segment(CoordSystem2, CoordSystem3) → k
  34. Segment(CoordSystem2, CoordSystem1) → l
  35. Sequence(CoordSystem2 + ((i * 0.5), 0), i, 0, 28) → l1
  36. Sequence(Segment[l1(i), l1(i) + (0, 4.5)], i, 1, Length[l1]) → l2
  37. Sequence(CoordSystem2 + (0, (i * 0.5)), i, 0, 9) → l3
  38. Sequence(Segment[l3(i), l3(i) + (14, 0)], i, 1, Length[l3]) → l4
  39. Angle(C, E, A) → α
  40. Angle(C1, F, A1) → β
  41. SelectedIndex(DD) → index3
  42. Text("\textsf{||}", Midpoint[D, C] + (0, 0.05), false, true, 0, 0) → Text7
  43. Text("\textsf{||}", Midpoint[A, B] + (0, 0.05), false, true, 0, 0) → Text8
  44. Text("\textsf{||}", Midpoint[D1, C1] + (0, 0.05), false, true, 0, 0) → Text5
  45. Text("\textsf{||}", Midpoint[B1, A1] + (0, 0.05), false, true, 0, 0) → Text6
  46. Text(Text12, G, false, true, 0, 0) → Text14
  47. Text(Text13, H, false, true, 0, 0) → Text15
  48. Text(Text3, I, false, true, -1, 0) → Text17
  49. Text(Text4, J, false, true, 1, 0) → Text18

AI Drawing Prompt Reference

Draw a trapezoid to demonstrate how its area changes with the lengths of the parallel sides and the height. The parallel sides and height of the trapezoid can be adjusted, with different colors and labels used to indicate them. Below the trapezoid, draw a coordinate system and plot a function graph showing the change in trapezoid area with varying parallel side lengths and heights. Label the values of the parallel side lengths and height next to the trapezoid and the values on the function graph in the coordinate system.
The prompt above was compiled from the original drawing commands and is for reference only.