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Area of a Kite

Area of a Kite
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2018-03-05 03:09
PolygonAngleGeometric Construction
This example demonstrates how to calculate the area of a kite by constructing its diagonals. Key math concepts include kite properties, perpendicular bisectors of diagonals, Pythagorean theorem, and triangle area formulas. GeoGebra commands and objects like Segment, LineBisector, Point, Intersect, Polygon, Midpoint, Rotate, and Angle are used to construct the kite and measure its diagonals. Suitable for middle school students and geometry teaching.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. LineBisector(f) → g
  3. Point(g) → C
  4. Point(g) → D
  5. Intersect(g, f) → E
  6. Polygon(A, E, C) → t1_1, c, a, e
  7. Polygon(C, E, B) → t2_1, b, c_1, e_1
  8. Polygon(A, D, E) → t3_1, e_2, a_1, d
  9. Polygon(D, E, B) → t4_1, b_1, d_1, e_3
  10. Midpoint(e) → F
  11. Midpoint(e_2) → G
  12. Midpoint(e_3) → H
  13. Midpoint(e_1) → I
  14. Rotate(A, t1, F) → A'
  15. Rotate(E, t1, F) → E'
  16. Rotate(C, t1, F) → C'
  17. Polygon(A', E', C') → t5, c', a', e'
  18. Rotate(C, t2, I) → C'_1
  19. Rotate(E, t2, I) → E'_1
  20. Rotate(B, t2, I) → B'
  21. Polygon(C'_1, E'_1, B') → t6, b', c'_1, e'_1
  22. Rotate(D, t3, H) → D'
  23. Rotate(E, t3, H) → E'_2
  24. Rotate(B, t3, H) → B'_1
  25. Polygon(D', E'_2, B'_1) → t7, b'_1, d', e'_2
  26. Rotate(A, t4, G) → A'_1
  27. Rotate(D, t4, G) → D'_1
  28. Rotate(E, t4, G) → E'_3
  29. Polygon(A'_1, D'_1, E'_3) → t8, e'_3, a'_1, d'_1
  30. Angle(C, E, A) → α
  31. Angle(C, E'_1, B) → β