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Area of a Rhombus by Andrea Siwik

Area of a Rhombus by Andrea Siwik
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2019-03-19 22:59
Geometric Construction
This example demonstrates the calculation of the area of a rhombus. The key mathematical concepts involved include the properties of a rhombus, the area formula, and geometric construction techniques. The construction involves using GeoGebra commands such as Segment, LineBisector, Intersect, etc. to create the rhombus shape. It is suitable for middle or high school mathematics learning, helping students understand the relationship between the area of a rhombus and its side length and height, as well as mastering basic geometric construction steps.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. LineBisector(a) → b
  3. Intersect(b, a) → C
  4. Point(b) → D
  5. Circle(C, D) → c
  6. Intersect(c, b, 2) → E
  7. Polygon(A, C, E) → poly2, e_1, a_2, c_1
  8. Polygon(C, B, E) → poly3, e_2, c_2, b_2
  9. Polygon(D, A, B) → poly1, b_1, d, a_1
  10. Vector(A, ((r * x(D)), (r * y(D)))) → u
  11. Translate(A, u) → A'
  12. Translate(C, u) → C'_1
  13. Translate(E, u) → E'_1
  14. Polygon(A', C'_1, E'_1) → poly2', e', a', c'
  15. Line(D, B) → e
  16. Translate(B, u) → B'_1
  17. Vector(B, B'_1) → v
  18. OrthogonalLine(B, d) → f
  19. Mirror(B'_1, f) → B''
  20. Vector(B, B'') → w
  21. Translate(C, w) → C'
  22. Translate(B, w) → B'
  23. Translate(E, w) → E'
  24. Polygon(C', B', E') → poly3', e'_1, c'_1, b'
  25. Segment(D, C) → g
  26. OrthogonalLine(F, b') → h
  27. Circle(F, (0.1 * b')) → k
  28. Intersect(k, h) → G, H
  29. Line(H, b') → i
  30. Circle(H, (0.5 * b')) → p
  31. Intersect(p, i) → I, J
  32. Vector(H, J) → z
  33. Vector(H, I) → j
  34. Circle(D, (0.1 * b')) → q
  35. Intersect(q, b) → K, L
  36. Line(L, e') → l
  37. Circle(L, e') → s
  38. Intersect(s, l) → M, N
  39. Vector(L, M) → m
  40. Vector(L, N) → n
  41. Intersect(a_1, b_1) → O
  42. Intersect(c', a') → P
  43. Point(a) → Q
  44. Intersect(a, a_1) → R
  45. Segment(Q, R) → d_1
  46. Line(A, B) → f_1
  47. Line(D, f_1) → g_1
  48. Translate(D, w) → D'
  49. OrthogonalLine(E', g_1) → h_1
  50. Intersect(g_1, h_1) → T
  51. Segment(T, E') → t