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Kite Area Demonstration by Craig Mackey

Kite Area Demonstration by Craig Mackey
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2020-04-01 14:52
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to dynamically calculate the area of a kite by exploring its properties and the area formula. Key math concepts include kite diagonals, area calculation, and coordinate geometry construction. GeoGebra commands and objects used are Line, Point, OrthogonalLine, Segment, Midpoint, Mirror, Vector, Polygon, Intersect, Translate. Suitable for high school mathematics teaching to visually understand the derivation of the kite area formula.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Point(a) → C
  3. OrthogonalLine(C, a) → b
  4. Point(b) → D
  5. Segment(B, D) → p
  6. Midpoint(p) → E
  7. Mirror(D, a) → D'
  8. Segment(D', B) → n
  9. Midpoint(n) → J
  10. Vector(J, E) → u
  11. Polygon(A, D, B, D') → poly1, a_1, d, b_1, d'
  12. OrthogonalLine(B, a) → c
  13. OrthogonalLine(D, b) → e
  14. OrthogonalLine(A, a) → f
  15. OrthogonalLine(D', b) → g
  16. Intersect(f, g) → F
  17. Intersect(c, g) → G
  18. Intersect(c, e) → H
  19. Intersect(e, f) → I
  20. Segment(D, D') → i
  21. Segment(F, G) → j
  22. Segment(G, H) → k
  23. Segment(H, I) → l
  24. Segment(I, F) → m
  25. Segment(A, B) → h
  26. Polygon(D', C, B) → poly2, b_2, d'_1, c_1
  27. Midpoint(n) → R
  28. Translate(R, Vector[o * u]) → R'
  29. Line(J, m) → r
  30. Segment(C, B) → s
  31. Midpoint(s) → S
  32. Vector(C, B) → v
  33. Translate(C, Vector[o * (u + v)]) → C'
  34. Translate(B, Vector[o * (u - v)]) → B'
  35. Vector(D', B) → w
  36. Translate(D', Vector[o * w]) → D''
  37. Polygon(D'', C', B') → poly3, b', d'', c'
  38. Vector(D', A) → z
  39. Vector(A, I) → q
  40. Vector(C, A) → t
  41. Translate(D', Vector[o * z]) → D''_1
  42. Translate(C, Vector[o * (t + q)]) → C'_1
  43. Translate(A, Vector[o * (q - t)]) → A'
  44. Polygon(D''_1, C'_1, A') → poly4, a', d''_1, c'_1
  45. Polygon(A, B, D) → poly5, d_1, a_2, b_3
  46. Polygon(D', B, C) → poly6, c_2, d'_2, b_4
  47. Polygon(D', C, A) → poly7, a_3, d'_3, c_3

AI Drawing Prompt Reference

Draw a kite and demonstrate its area calculation using its diagonals. Start by creating line segments AB and CD, then find their midpoints E and J. Next, use reflections and rotations to create D' and C', and construct new polygons with them. Finally, adjust the positions of the points to ensure the area can be calculated using the diagonals.
The prompt above was compiled from the original drawing commands and is for reference only.