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Deltoid Area Formula Calculation and Verification

Deltoid Area Formula Calculation and Verification
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2023-09-07 13:37
PolygonAngleGeometric ConstructionGraphing
In collections Deltoid - Flächeninhalt und Umkehraufgaben Deltoid - Flächeninhalt
This GeoGebra example demonstrates the deltoid (kite) area formula A=(e×f)/2, showing the relationship between diagonal lengths and area. Construction uses: Polygon for the quadrilateral, Segment for diagonals, Circle for auxiliary construction showing perpendicular bisecting diagonals, Angle to verify right angles, Text for formula display. Includes three interactive tasks: ①multiple-choice formula verification; ②error analysis and correction; ③geometric explanation of the formula. Suitable for grades 5-6 students learning area calculations of special quadrilaterals, developing geometric intuition and formula application skills.

GeoGebra Commands & Parameters

  1. SelectedIndex(DropDown2) → index2
  2. Circle(Tri1M, Length[Segment[A, M]]) → HelperKreis4
  3. Point(HelperKreis4) → Tri1Anchor
  4. Rotate(Tri1Anchor, 90°, Tri1M) → I'
  5. Spline({M, I, H}, 3) → a
  6. Circle(Tri4M, Length[Segment[A, M]]) → HelperKreis1
  7. Circle(Tri2M, Length[Segment[C, M]]) → HelperKreis2
  8. Circle(Tri3M, Length[Segment[C, M]]) → HelperKreis3
  9. Point(HelperKreis2) → Tri2Anchor
  10. Point(HelperKreis3) → Tri3Anchor
  11. Point(HelperKreis1) → Tri4Anchor
  12. Rotate(Tri4Anchor, -90°, Tri4M) → L'
  13. Angle(Tri4Anchor, Tri4M, L') → α
  14. Angle(Tri1Anchor, Tri1M, I') → β
  15. Rotate(Tri2Anchor, -90°, Tri2M) → J'
  16. Angle(J', Tri2M, Tri2Anchor) → γ
  17. Rotate(Tri3Anchor, 90°, Tri3M) → K'
  18. Angle(Tri3Anchor, Tri3M, K') → δ
  19. Polygon(Tri2E, Tri2M, Tri2Anchor) → d1, j, o, g
  20. Polygon(Tri1E, Tri1Anchor, Tri1M) → d2, f_1, n, i
  21. Polygon(Tri3M, Tri3Anchor, Tri3E) → d3, p, h, k
  22. Polygon(Tri4M, Tri4Anchor, Tri4E) → d4, q, e_1, l
  23. Polygon(E, F, G) → AnimOrange, g_1, e, f
  24. Rotate(AnimTri1Anchor + Vector[M, B], ε, AnimTri1Anchor) → AnimTri1E1
  25. Spline({M, O, N}, 3) → b
  26. Rotate(AnimTri1Anchor + (Vector[M, A] * (-helperinvert)), ε, AnimTri1Anchor) → AnimTri1E2
  27. SelectedIndex(DropDown) → index1
  28. Midpoint(Corner[Texte, 1], Corner[Texte, 3]) → TextePos
  29. Midpoint(Corner[Texte2, 1], Corner[Texte2, 3]) → Texte2Pos
  30. Midpoint(Corner[Textf2, 1], Corner[Textf2, 3]) → Textf2Pos
  31. Midpoint(Corner[Textf, 1], Corner[Textf, 3]) → TextfPos
  32. Polygon(ZuordnungVE1, ZuordnungVE2, ZuordnungVE3, ZuordnungVE4) → ZV1, zuordnungve1, zuordnungve2, zuordnungve3, zuordnungve4
  33. Polygon(ZuordnungV2E1, ZuordnungV2E2, ZuordnungV2E3, ZuordnungV2E4) → ZV2, zuordnungv2e1, zuordnungv2e2, zuordnungv2e3, zuordnungv2e4
  34. IsInRegion(Textf2Pos, ZV2) → correctZuordnung
  35. Midpoint(M, D) → Q
  36. Rotate(Triforce1 + Vector[M, D], (neoanim1 * 180°), Triforce1) → R
  37. Rotate(Triforce1 + Vector[M, A], (neoanim1 * 180°), Triforce1) → S
  38. Rotate(Triforce2 + Vector[M, D], (neoanim2 * 180°), Triforce2) → T
  39. Rotate(Triforce2 + Vector[M, C], (neoanim2 * 180°), Triforce2) → U
  40. SelectedIndex(DD3) → index3
  41. SelectedIndex(DD4) → index4
  42. Point(AnimOrangeKanten) → W
  43. Circle(W, 0.5) → validateC1
  44. Circle(F, 0.5) → validateC2
  45. Circle(V, 0.5) → validateC3
  46. Circle(Triforce1, 0.5) → validateC4
  47. Circle(G, 0.5) → validateC5
  48. Circle(Triforce2, 0.5) → validateC6
  49. Angle(D, M, A) → ζ
  50. Segment(A, C) → m
  51. Segment(Midpoint[B, D], D) → r
  52. Segment(E_1, E_1 + (4, 0)) → s
  53. Point(s, distanzAnim / 5) → F_1
  54. Text(Text10, F_1, false, true, 0, 0) → Text18
  55. Segment(G_1, G_1 + (0, (-LA1))) → t
  56. Segment(H_1, H_1 + (0, -0.92)) → h_1
  57. CircleArc(Tri1M, Rotate[Tri1Anchor, (-williwingl), Tri1M], Rotate[Tri1Anchor, williwingl, Tri1M]) → c_1
  58. Segment(Rotate[Tri1Anchor, williwingl - 1°, Tri1M], Rotate[Tri1Anchor, williwingl, Tri1M]) → i_1
  59. Segment(Rotate[Tri1Anchor, (-williwingl) + 1°, Tri1M], Rotate[Tri1Anchor, (-williwingl), Tri1M]) → j_1

AI Drawing Prompt Reference

Draw a kite shape to demonstrate the relationship between its diagonals and area, with the area formula A=(e×f)/2. Start by constructing the quadrilateral of the kite, then draw the diagonals and use circles to show the perpendicular bisectors of the diagonals. Verify right angles and display the formula. Include interactive tasks for students to check the formula, analyze errors, and explain the formula, suitable for 5-6 grade students.
The prompt above was compiled from the original drawing commands and is for reference only.