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Area of a Rhombus by user3375

Area of a Rhombus by user3375
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2013-08-15 09:14
PolygonCoordinate GeometryGeometric Construction
In collections Deriving area formulas for Geometry Area Investigations Deriving area formulas for Geometry
This example demonstrates how to calculate the area of a rhombus using geometric construction. Key mathematical concepts include the properties of a rhombus and its area formula. Using GeoGebra commands such as Point, Segment, Polygon, etc., the construction process is dynamically shown. Suitable for middle school and above students to learn geometry and area calculation.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → b
  3. Circle(A, a) → c
  4. Point(c) → C
  5. Segment(A, C) → d
  6. Circle(C, a) → e
  7. Line(C, b) → f
  8. Intersect(e, f, 2) → D
  9. Segment(C, D) → g
  10. Segment(D, B) → h
  11. Segment(A, D) → m
  12. Segment(C, B) → n
  13. Intersect(m, n) → E
  14. Polygon(C, E, D) → P, d_1, c_1, e_1
  15. Polygon(C, E, A) → Q, a_1, c_2, e_2
  16. Polygon(A, E, B) → R, b_1, a_2, e_3
  17. Polygon(B, D, E) → S, e_4, b_2, d_2
  18. Midpoint(D, C) → F
  19. Midpoint(D, B) → G
  20. Midpoint(A, B) → H
  21. Midpoint(A, C) → I
  22. Mirror(C, I) → C'
  23. Mirror(E, I) → E'
  24. Mirror(A, I) → A'
  25. Mirror(C, F) → C'_1
  26. Mirror(E, F) → E'_1
  27. Mirror(D, F) → D'
  28. Mirror(B, G) → B'
  29. Mirror(D, G) → D'_1
  30. Mirror(E, G) → E'_2
  31. Mirror(A, H) → A'_1
  32. Mirror(E, H) → E'_3
  33. Mirror(B, H) → B'_1
  34. Rotate(C, α, I) → C'_2
  35. Rotate(E, α, I) → E'_4
  36. Rotate(A, α, I) → A'_2
  37. Polygon(C'_2, E'_4, A'_2) → Q', a'_2, c'_2, e'_4
  38. Rotate(C, -β, F) → C'_3
  39. Rotate(E, -β, F) → E'_5
  40. Rotate(D, -β, F) → D'_2
  41. Polygon(C'_3, E'_5, D'_2) → P', d'_2, c'_3, e'_5
  42. Rotate(A, γ, H) → A'_3
  43. Rotate(E, γ, H) → E'_6
  44. Rotate(B, γ, H) → B'_2
  45. Polygon(A'_3, E'_6, B'_2) → R', b'_2, a'_3, e'_6
  46. Rotate(B, -δ, G) → B'_3
  47. Rotate(D, -δ, G) → D'_3
  48. Rotate(E, -δ, G) → E'_7
  49. Polygon(B'_3, D'_3, E'_7) → S', e'_7, b'_3, d'_3