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Interactive Practice: Calculating the Area of a Parallelogram

Interactive Practice: Calculating the Area of a Parallelogram
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2024-02-06 18:11
PolygonAngleTransformationGeometric ConstructionSlider Animation
In collections Parallelogramm und Raute: Flächeninhalt
This GeoGebra example demonstrates how to calculate the area of a parallelogram through an interactive exercise. It focuses on the core mathematical concept of the parallelogram area formula (base times height) and its application to special quadrilaterals such as parallelograms, trapezoids, kites, and rhombi. The construction uses GeoGebra commands including Polygon to create the parallelogram, OrthogonalLine and Intersect to construct the height, Text and InputBox for user input and feedback, Shuffle and Rotate to randomize problem variations, If and Join for logical control, Circle and Angle for visual aids, and buttons like validate, showanswer, and showSolution to enable interactive checking. Suitable for students in grades 5-6 or early secondary school, this resource supports classroom practice and self-study, enhancing skills in applying and justifying area formulas.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle({1, 2}) → ModusList, {1, 2}
  4. Shuffle(Sequence[i, i, 24, round((rad2 * 10))]) → Rad1List, {28, 25, 27, 24, 29, 26}
  5. Shuffle(Sequence[i, i, 1, 360]) → GradList, {295, 23, 288, 341, 194, 244, 24, 66, 308, 9, 274, 114, 214, 85, 35, 163, 178, 104, 47, 28, 128, 200, 105, 147, 316, 205, 6, 14, 172, 154, 267, 329, 249, 275, 179, 65, 42, 25, 73, 40, 79, 141, 33, 121, 313, 58, 253, 76, 211, 353, 266, 348, 224, 238, 113, 270, 101, 213, 86, 8, 248, 60, 228, 227, 340, 100, 212, 160, 44, 107, 115, 124, 317, 109, 90, 321, 27, 166, 272, 180, 309, 171, 280, 68, 239, 48, 284, 277, 129, 273, 196, 336, 217, 89, 318, 127, 332, 43, 246, 207, 258, 161, 83, 291, 243, 97, 12, 1, 360, 136, 328, 36, 330, 257, 55, 91, 279, 22, 235, 310, 87, 131, 138, 315, 61, 165, 93, 110, 38, 153, 236, 146, 53, 4, 148, 123, 116, 223, 289, 149, 201, 222, 209, 345, 290, 281, 255, 169, 301, 287, 184, 269, 69, 16, 202, 74, 314, 350, 240, 334, 215, 19, 234, 210, 191, 271, 198, 241, 164, 352, 5, 260, 117, 219, 188, 199, 15, 218, 263, 185, 286, 99, 343, 59, 133, 84, 338, 142, 344, 135, 203, 7, 285, 168, 134, 54, 21, 333, 92, 29, 187, 111, 259, 119, 226, 34, 11, 307, 37, 158, 331, 192, 102, 78, 220, 355, 346, 167, 319, 103, 3, 262, 189, 32, 72, 88, 195, 276, 62, 296, 322, 304, 51, 326, 155, 337, 177, 294, 323, 354, 251, 13, 170, 339, 264, 306, 325, 144, 186, 45, 122, 181, 256, 342, 10, 298, 293, 81, 230, 156, 75, 98, 204, 96, 80, 299, 2, 265, 94, 193, 31, 250, 311, 162, 173, 26, 175, 229, 245, 237, 283, 182, 358, 71, 312, 190, 225, 64, 139, 356, 30, 359, 126, 18, 49, 320, 125, 159, 140, 302, 347, 176, 118, 305, 268, 41, 206, 233, 70, 132, 143, 232, 52, 82, 261, 17, 208, 216, 120, 108, 67, 50, 57, 297, 197, 231, 335, 300, 351, 221, 183, 252, 150, 292, 95, 46, 77, 157, 278, 357, 247, 152, 56, 39, 63, 145, 137, 106, 327, 242, 20, 349, 303, 130, 282, 174, 324, 254, 151, 112}
  6. Rotate(DrehAnchor, grad°, M) → A
  7. Shuffle(Join[{Sequence[i, i, 30, 40], Sequence[i, i, 75, 85]}]) → GradList2, {38, 33, 30, 82, 40, 31, 76, 80, 85, 37, 77, 78, 81, 34, 39, 79, 75, 36, 35, 84, 83, 32}
  8. Rotate(M, grad2°, A) → D
  9. Rotate(M, grad2°, C) → B_{1}
  10. Polygon(B_{1}, C, D, A) → v1, m'_{1}, c_1, m', a
  11. OrthogonalLine(D, a) → f
  12. OrthogonalLine(D, m'_{1}) → g
  13. OrthogonalLine(C, a) → h
  14. OrthogonalLine(C, m') → i
  15. Intersect(h, a) → HöheaCP
  16. Intersect(i, m') → HöhebCP
  17. Intersect(g, m'_{1}) → HöhebDP
  18. Intersect(a, f) → HöheaDP
  19. If(modus ≟ 1 ∧ Defined[Hoehea(1)], Length[Hoehea(1)], modus ≟ 1 ∧ (¬Defined[Hoehea(1)]), Length[Hoehea(2)], modus ≟ 2 ∧ Defined[Hoeheb(1)], Length[Hoeheb(1)], modus ≟ 2 ∧ (¬Defined[Hoeheb(1)]), Length[Hoeheb(2)]) → hwertraw
  20. Shuffle(1…8) → ExNumList, {7, 1, 5, 2, 3, 8, 4, 6}
  21. Join({{2, 8}, ExNumList \ {2, 8}}) → ExNumListReal
  22. If(exNum ∈ {1, 2, 7, 8}, (Angabea * Angabeh), (Angabeb * Angabeh)) → sol
  23. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  24. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 6, 9, 4, 8, 2, 9, 3, 2, 9, 0, 8, 8, 5, 7, 5, 1, 0, 4, 3, 10, 3, 5, 5, 1, 5, 2, 9, 8, 5, 1, 4, 5, 0, 3, 0, 8, 7, 1, 2, 5, 6, 3, 4, 10, 2, 9, 5, 3, 8, 0, 6, 4, 6, 10, 7, 0, 8, 10, 10, 10, 8, 8, 4, 0, 6, 9, 4, 10, 2, 7, 3, 1, 4, 8, 7, 7, 10, 3, 1, 1, 5, 4, 8, 4, 5, 6, 10, 7, 9, 5, 8, 2, 5, 1, 6, 1, 4, 1, 6}
  25. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  26. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {4, 1, 8, 5, 6, 0, 9, 8, 7, 3, 6, 8, 5, 5, 2, 1, 7, 3, 4, 3, 1, 10, 4, 7, 10, 9, 6, 3, 1, 8, 2, 0, 6, 2, 6, 6, 4, 4, 8, 2, 1, 0, 1, 5, 9, 0, 4, 9, 8, 0, 6, 6, 0, 6, 9, 4, 7, 3, 10, 2, 9, 8, 1, 3, 3, 0, 2, 1, 2, 10, 7, 0, 0, 0, 2, 0, 1, 1, 2, 4, 3, 7, 3, 8, 1, 9, 3, 6, 10, 6, 8, 8, 4, 5, 2, 9, 9, 1, 8, 0}
  27. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  28. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  29. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  30. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  31. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  32. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  33. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  34. Defined(input1) → fixed
  35. Circle(M, rad2) → c
  36. Circle(M, rad1) → d
  37. Angle(M, A, D) → α
  38. Angle(M, C, B_{1}) → β
  39. Text("\textsf{A}", F, false, true, 0, 0) → Text2
  40. Text("\textsf{B}", G, false, true, 0, 0) → Text3
  41. Text("\textsf{C}", E, false, true, 0, 0) → Text4
  42. Text("\textsf{D}", H, false, true, 0, 0) → Text5
  43. If(Defined[Segment[HöheaCP, C]], Midpoint[Segment[HöheaCP, C]], Midpoint[Segment[HöheaDP, D]]) → Beschha
  44. If(Defined[Segment[HöhebCP, C]], Midpoint[Segment[HöhebCP, C]], Midpoint[Segment[HöhebDP, D]]) → Beschhb
  45. Text(Beschh, If[modus ≟ 1, J, I], false, true, 0, 0) → Text6
  46. If(modus ≟ 1, (awert * hwert), (bwert * hwert)) → solwert
  47. Angle(C, HöhebCP, D) → γ
  48. Angle(D, HöheaDP, A) → δ
  49. Angle(D, HöhebDP, B_{1}) → ε
  50. Angle(C, HöheaCP, A) → ζ
  51. Rotate(ParaPB, alphakonst°, ParaPA) → L'
  52. Circle(ParaPA, bkonst) → e
  53. Ray(ParaPA, L') → j
  54. Intersect(e, j) → ParaPD,
  55. If(x(ParaPA) < x(ParaPD), (x(ParaPD), y(ParaPA)), (x(ParaPA), y(ParaPD))) → ParaPHelper1
  56. Angle(ParaPB, ParaPA, ParaPHelper1) → η
  57. Angle(ParaPD, ParaPHelper1, ParaPA) → θ
  58. If(x(ParaPD) < x(ParaPA), Segment[ParaPA, ParaPHelper1], Segment[ParaPD, ParaPHelper1]) → hoehea
  59. Segment(ParaPA, ParaPD) → k
  60. OrthogonalLine(ParaPA, k) → l
  61. Segment(ParaPB, ParaPC) → m
  62. OrthogonalLine(ParaPB, m) → n
  63. If(Defined[Intersect[l, Ray[ParaPB, ParaPC]]], Intersect[l, Ray[ParaPB, ParaPC]], Intersect[n, Segment[ParaPD, ParaPA]]) → ParaPHelper2
  64. If(Defined[Intersect[l, Ray[ParaPB, ParaPC]]], Segment[ParaPA, ParaPHelper2], Segment[ParaPB, ParaPHelper2]) → hoeheb
  65. Angle(ParaPB, ParaPHelper2, ParaPD) → williwingl
  66. Angle(ParaPA, ParaPHelper2, ParaPB) → κ
  67. Midpoint(ParaPA, ParaPB) → N
  68. Midpoint(ParaPC, ParaPB) → O
  69. Midpoint(ParaPA, ParaPD) → P
  70. Midpoint(ParaPD, ParaPC) → Q
  71. Text(Text9, R, false, true, 0, 0) → Text11
  72. Text(Text9, U, false, true, 0, 0) → Text12
  73. Text(Text10, S, false, true, 0, 0) → Text13
  74. Text(Text10, T, false, true, 0, 0) → Text14
  75. Midpoint(ParaPA, ParaPB) → V
  76. If(exNum ∈ {1, 2, 7, 8}, Segment[ParaPD, ParaPC], Segment[ParaPB, ParaPC]) → HintStrecke

AI Drawing Prompt Reference

Draw a quadrilateral in the plane formed by four points, arranged as a parallelogram so that opposite sides are parallel and the figure can vary by rotating one side about a pivot. Construct the height by dropping perpendicular lines from appropriate vertices to the opposite sides, then mark the foot points and form the segment that represents the height. Add angle indicators at the key vertex regions between the base direction and the lines used for the height. Label the four vertices with simple text, and include input/feedback text areas for the user to enter lengths (base and height) and to show a computed solution or confirmation. Provide the diagram in two possible configuration modes by switching the correspondence used for the height construction.
The prompt above was compiled from the original drawing commands and is for reference only.