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Rhombus Area Demonstration

Rhombus Area Demonstration
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2020-04-01 14:51
PolygonVectorTrigonometryGeometric Construction
This example demonstrates how to calculate the area of a rhombus by constructing its diagonals. Key math concepts include rhombus properties, perpendicular bisectors of diagonals, triangle area formula, and vector operations. GeoGebra commands/objects used in construction are Segment, Midpoint, OrthogonalLine, Point, Mirror, Vector, Translate, Polygon, and Rotate. Suitable for high school mathematics teaching or self-learning to understand the derivation of the rhombus area formula.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Midpoint(a) → C
  3. OrthogonalLine(C, a) → b
  4. Point(b) → D
  5. Mirror(D, C) → D'
  6. Vector(C, D') → u
  7. Translate(B, u) → B'
  8. Vector(C, B') → w
  9. Segment(A, D') → c
  10. Segment(D', B) → d
  11. Segment(B, D) → e
  12. Segment(D, A) → f
  13. Translate(A, u) → A'
  14. Segment(A', B') → a'
  15. Vector(C, D) → v
  16. Translate(A, v) → A'_1
  17. Translate(B, v) → B'_1
  18. Segment(A'_1, B'_1) → a'_1
  19. Segment(A', A'_1) → g
  20. Segment(D', D) → h
  21. Segment(B', B'_1) → i
  22. Polygon(A, B, D') → poly2, d', a_1, b_1
  23. Polygon(A, C, D) → poly1, d_1, a_2, c_1
  24. Segment(C, B') → j
  25. Translate(C, Vector[k * w]) → C'
  26. Translate(D, Vector[k * w]) → D'_1
  27. Translate(A, Vector[k * w]) → A'_2
  28. Polygon(A'_2, C', D'_1) → poly1', d'_1, a'_2, c'
  29. Vector(C, A') → z
  30. Polygon(D, C, B) → poly3, b_2, d_2, c_2
  31. Translate(D, Vector[k * z]) → D'_2
  32. Translate(C, Vector[k * z]) → C'_1
  33. Translate(B, Vector[k * z]) → B'_2
  34. Polygon(D'_2, C'_1, B'_2) → poly3', b'_2, d'_2, c'_1
  35. Segment(A', B') → l
  36. Point(b) → E
  37. Vector(D, E) → n
  38. Translate(A'_1, n) → F
  39. Translate(B'_1, n) → G
  40. Vector(E, G) → q
  41. Vector(E, F) → r
  42. Rotate(n, 270*°, D) → n'
  43. Translate(A', n') → A''
  44. Translate(A'_1, n') → H
  45. Midpoint(A'', H) → I
  46. Vector(I, A'') → m
  47. Vector(I, H) → p