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Area of Parallelogram in Grid (Level 2)

Area of Parallelogram in Grid (Level 2)
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2024-02-06 18:09
PolygonVectorCoordinate GeometryGeometric Construction
In collections Parallelogramm und Raute: Flächeninhalt
This example demonstrates how to calculate the area of a parallelogram in a coordinate grid. Key mathematical concepts include the area formula for parallelograms (base × height), geometric interpretation of grid coordinates, and the relationship between vector cross product and area. Construction highlights: Using Polygon command to construct the parallelogram, Segment for auxiliary lines showing base and height, Translate/Midpoint for geometric transformations, Random/Shuffle for generating random coordinates, and InputBox for interactive validation. Suitable for grades 5-6, this activity helps students master area formulas for special quadrilaterals and develops geometric intuition through coordinate visualization.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[Random[7, coordheight - 2], m, 1, 100]) → randomNosForX, {7, 8, 8, 8, 8, 10, 7, 8, 8, 9, 7, 8, 7, 10, 8, 7, 7, 7, 10, 7, 7, 7, 10, 7, 7, 8, 7, 7, 7, 8, 7, 7, 7, 10, 10, 9, 10, 10, 10, 9, 8, 8, 8, 9, 8, 7, 8, 8, 9, 9, 7, 7, 9, 7, 7, 9, 8, 8, 9, 8, 7, 9, 7, 7, 9, 10, 9, 7, 8, 9, 8, 7, 9, 8, 9, 7, 10, 10, 9, 7, 7, 7, 7, 9, 10, 7, 9, 9, 8, 9, 8, 10, 9, 8, 9, 7, 7, 9, 9, 8}
  2. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  3. Shuffle(Sequence[Random[4, coordwidth - 2], m, 1, 100]) → randomNosForY, {7, 10, 7, 9, 6, 8, 7, 9, 4, 10, 9, 4, 8, 4, 6, 10, 10, 7, 7, 6, 8, 5, 9, 9, 9, 9, 6, 9, 6, 8, 9, 5, 10, 9, 8, 10, 8, 4, 9, 7, 10, 6, 7, 7, 6, 8, 5, 4, 10, 10, 9, 10, 9, 6, 10, 8, 7, 7, 5, 10, 6, 8, 6, 7, 4, 7, 5, 6, 4, 6, 8, 9, 4, 6, 9, 10, 5, 8, 10, 4, 10, 6, 5, 6, 10, 10, 8, 6, 10, 8, 4, 6, 7, 5, 10, 7, 8, 7, 6, 10}
  4. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  5. Textfield(input1) → InputBox1
  6. Textfield(input2) → InputBox2
  7. Shuffle(Sequence[i, i, 6, 12] \ {axold}) → AxList, {12, 10, 9, 11, 8, 6, 7}
  8. Shuffle(Sequence[i, i, 1, 12] \ {ax - 2, ax - 1, ax, ax + 1, ax + 2}) → CxList, {1, 8, 4, 7, 6, 9, 2, 5, 3}
  9. Shuffle(Sequence[i, i, 2, abs(cx - ax)] \ {abs(cx - ax)}) → LaengeaList, {8, 3, 7, 5, 2, 6, 4, 9, 10}
  10. Shuffle(Sequence[i, i, 1, 9] \ {ayold}) → AyList, {9, 4, 2, 7, 6, 8, 3, 1, 5}
  11. Shuffle(Sequence[i, i, 1, 12] \ {ay - 2, ay - 1, ay, ay + 1, ay + 2}) → CyList, {6, 1, 12, 3, 2, 5, 4}
  12. If(cx < ax, C + (size * (laengea, 0)), C - (size * (laengea, 0))) → B
  13. If(cx < ax, A - (size * (laengea, 0)), A + (size * (laengea, 0))) → D
  14. Polygon(C, B, A, D) → v2, j, k, l, m
  15. OrthogonalLine(D, l) → n
  16. Intersect(n, Line[C, B]) → E
  17. Segment(D, E) → p
  18. Shuffle({0.5, 1.5, 2, 3}) → EinheitsLList, {0.5, 2, 1.5, 3}
  19. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  20. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  21. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  22. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  23. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  24. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  25. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  26. Defined(input3) → fixed
  27. Flatten(Sequence[Sequence[O + (m * (size, 0)) + (j * (0, size)), m, 0, coordwidth - 1], j, 0, coordheight - 1]) → listPoints
  28. Zip(Polygon[P, P + (0, size), P + (0, size) + (size, 0), P + (size, 0)], P, listPoints) → listCoords
  29. Segment(P1, P3) → es
  30. Random(2, numX - 2) → prop
  31. Segment(P4, P2) → fs
  32. Segment(G1, G2) → g
  33. Translate(Segment[(0, -0.1), (0, 0.1)], G1) → h
  34. Translate(Segment[(0, -0.1), (0, 0.1)], G2) → i
  35. Intersect(es, fs) → S
  36. Textfield(input3) → InputBox3
  37. Shuffle({1, 2}) → ModusList, {2, 1}
  38. If(y(C) < y(D), Midpoint[C, B], Midpoint[D, A]) → MittelpunktUnten
  39. If(x(A) > x(D), Midpoint[A, B], Midpoint[D, C]) → MittelpunktRechts
  40. Midpoint(D, B) → M
  41. Text(BeschTextb, F, false, true, 0, 0) → Text3
  42. Text(BeschTexta, G, false, true, 0, 0) → Text4
  43. If(x(E) > x(B) ∧ y(B) > y(A) ∨ x(B) < x(E) ∧ y(B) < y(A), Midpoint[p] - (0.2, 0), Midpoint[p] + (0.2, 0)) → H
  44. Text(BeschTexth, H, false, true, 0, 0) → Text8
  45. Segment(C, E) → hintCE
  46. Segment(B, E) → hintBE
  47. Angle(A, D, E) → α
  48. Angle(C, E, D) → β
  49. Angle(D, E, C) → γ
  50. Angle(E, D, A) → δ
  51. Distance(H, F) → diff
  52. If(x(A) < x(D), Midpoint[A, B], Midpoint[D, C]) → MittelpunktLinks
  53. Text(BeschTextb, I, false, true, 0, 0) → Text16

AI Drawing Prompt Reference

Draw a parallelogram on a coordinate grid. Start by randomly selecting two points for the base and height, then construct the four vertices of the parallelogram. Draw auxiliary lines for the base and height, label the area formula, and calculate the area. Finally, add some auxiliary lines and angle markings to help understand the geometric relationships of the parallelogram.
The prompt above was compiled from the original drawing commands and is for reference only.