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Kite Area Calculation by toby mcfarlane

Kite Area Calculation by toby mcfarlane
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2015-10-09 15:07
PolygonTrigonometryGeometric Construction
This example demonstrates how to calculate the area of a kite by constructing its diagonals. Key math concepts include the properties of a kite, the perpendicular bisector relationship of diagonals, and the area formula. Construction highlights involve using GeoGebra commands like Segment, LineBisector, Point, Intersect, Polygon, Midpoint, Rotate to build the kite and its diagonals, and calculate the area through rotation and intersection points. Suitable for middle school and above students learning geometric constructions and area calculations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → AB
  2. LineBisector(AB) → b
  3. Point(b) → C
  4. Point(b) → D
  5. Segment(C, A) → c
  6. Segment(D, A) → d
  7. Segment(B, D) → e
  8. Segment(C, B) → f
  9. Intersect(b, AB) → E
  10. Polygon(C, E, A) → poly1, a_1, c_1, e_1
  11. Polygon(C, E, B) → poly2, b_1, c_2, e_2
  12. Polygon(A, E, D) → poly3, d_4, a_2, e_3
  13. Polygon(E, B, D) → poly4, d_3, e_4, b_2
  14. Midpoint(C, A) → F
  15. Midpoint(C, B) → G
  16. Midpoint(A, D) → H
  17. Midpoint(D, B) → I
  18. Rotate(A, rotateΔ, H) → A'
  19. Rotate(E, rotateΔ, H) → E'
  20. Rotate(D, rotateΔ, H) → D'
  21. Polygon(A', E', D') → poly3', d', a', e'
  22. Rotate(C, rotateΔ, F) → C'
  23. Rotate(E, rotateΔ, F) → E'_1
  24. Rotate(A, rotateΔ, F) → A'_1
  25. Polygon(C', E'_1, A'_1) → poly1', a'_1, c', e'_1
  26. Rotate(C, rotateΔ, G) → C'_1
  27. Rotate(E, rotateΔ, G) → E'_2
  28. Rotate(B, rotateΔ, G) → B'
  29. Polygon(C'_1, E'_2, B') → poly2', b', c'_1, e'_2
  30. Rotate(E, rotateΔ, I) → E'_3
  31. Rotate(B, rotateΔ, I) → B'_1
  32. Rotate(D, rotateΔ, I) → D'_1
  33. Polygon(E'_3, B'_1, D'_1) → poly4', d'_1, e'_3, b'_1
  34. Segment(D, C) → CD
  35. Midpoint(A, E) → J
  36. Midpoint(D, C) → K
  37. Angle(C, E, A) → α
  38. Midpoint(E, B) → L
  39. Segment(A, E) → a
  40. Segment(E, B) → g
  41. Segment(C, E) → i
  42. Segment(D, E) → j
  43. Polygon(D, C, A) → poly5, a_3, d_5, c_3
  44. Polygon(D, C, B) → poly6, b_3, d_6, c_4