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Area of a Kite by Edward Knote

Area of a Kite by Edward Knote
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2018-01-23 21:10
PolygonCoordinate GeometryGeometric Construction
In collections Area Formulas
This example demonstrates how to calculate the area of a kite using geometric construction. Key mathematical concepts include geometric construction, polygons, and area calculation. It uses commands such as point, segment, circle, intersection, polygon, midpoint, mirror, and rotate in GeoGebra. Suitable for middle school and above students or teachers to understand the properties of geometric shapes and area calculation methods.

GeoGebra Commands & Parameters

  1. Point(Circle[A, d_1]) → B
  2. Segment(A, B) → b_3
  3. Circle(A, B) → c
  4. Point(Circle[B, d_2]) → D
  5. Segment(B, D) → f
  6. Circle(D, B) → g
  7. Intersect(c, g, 1) → C
  8. Segment(A, C) → d
  9. Segment(C, D) → h
  10. Segment(A, D) → d_5
  11. Segment(B, C) → d_6
  12. Intersect(d_5, d_6) → E_1
  13. Polygon(C, E_1, D) → P, d_4, c_1, e_1
  14. Polygon(E_1, B, D) → Q, d_7, e_2, b_1
  15. Polygon(E_1, C, A) → R, a_1, e_3, c_2
  16. Polygon(E_1, B, A) → S, a_2, e_4, b_2
  17. Midpoint(C, D) → F
  18. Mirror(C, F) → C'
  19. Mirror(E_1, F) → E'
  20. Mirror(D, F) → D'
  21. Midpoint(A, C) → G
  22. Midpoint(A, B) → H
  23. Midpoint(B, D) → I
  24. Mirror(E_1, G) → E'_1
  25. Mirror(C, G) → C'_1
  26. Mirror(A, G) → A'
  27. Mirror(E_1, H) → E'_2
  28. Mirror(B, H) → B'
  29. Mirror(A, H) → A'_1
  30. Mirror(E_1, I) → E'_3
  31. Mirror(B, I) → B'_1
  32. Mirror(D, I) → D'_1
  33. Midpoint(B, C) → E
  34. Rotate(E_1, α, G) → E_1'
  35. Rotate(C, α, G) → C'_2
  36. Rotate(A, α, G) → A'_2
  37. Polygon(E_1', C'_2, A'_2) → R', a'_2, e_1', c'_2
  38. Rotate(C, (-β), F) → C'_4
  39. Rotate(E_1, (-β), F) → E_3
  40. Rotate(D, (-β), F) → D'_3
  41. Polygon(C'_4, E_3, D'_3) → P', d'_3, c'_4, e_5
  42. Rotate(E_1, γ, H) → E_2
  43. Rotate(B, γ, H) → B'_2
  44. Rotate(A, γ, H) → A'_3
  45. Polygon(E_2, B'_2, A'_3) → S', a'_3, e_6, b'_2
  46. Rotate(E_1, (-δ), I) → E_4
  47. Rotate(B, (-δ), I) → B'_3
  48. Rotate(D, (-δ), I) → D'_2
  49. Polygon(E_4, B'_3, D'_2) → Q', d'_2, e_7, b'_3