MathPlotAI Logo MathPlotAI

Areas of Parallelogram, Triangle, and Trapezium

Areas of Parallelogram, Triangle, and Trapezium
Loading the math board and drawing, please wait…
2020-02-17 12:44
PolygonVectorTrigonometryTransformationGeometric Construction
This example demonstrates how to calculate the areas of a parallelogram, triangle, and trapezium using geometric construction methods. Key mathematical concepts include similarity transformations, trigonometry, and vectors. Using GeoGebra commands such as point, line segment, rotation, mirror, and translation, the properties of these geometric shapes are visually illustrated. Suitable for middle and high school students studying geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(Circle[A, a]) → B
  3. Segment(A, B) → f
  4. Point(f) → C
  5. Point(Circle[C, b]) → D
  6. Segment(C, D) → g
  7. Rotate(D, 90°, C) → D'
  8. Segment(A, D') → h
  9. Line(B, h) → i
  10. Line(D', f) → j
  11. Intersect(i, j) → E
  12. OrthogonalLine(B, xAxis) → k
  13. OrthogonalLine(D', k) → l
  14. Intersect(k, l) → F
  15. Segment(B, F) → m
  16. Segment(C, D') → n
  17. Polygon(A, D', F, B) → q1, a_1, d', f_1, b_1
  18. Polygon(F, E, B) → t1, b_2, f_2, e
  19. OrthogonalLine(A, d') → p
  20. Line(E, D') → q
  21. Intersect(p, q) → G
  22. Point(Circle[F, μεταφορά]) → Α
  23. Segment(F, Α) → r
  24. Mirror(Α, F) → Α'
  25. Vector(F, Α') → u
  26. Translate(F, u) → F'
  27. Translate(E, u) → E'
  28. Translate(B, u) → B'
  29. Polygon(F', E', B') → t1', b', f', e'
  30. Point(xAxis) → Β
  31. Point(Circle[Β, a]) → Γ
  32. Segment(Β, Γ) → s
  33. Point(s) → Δ
  34. Point(Circle[Δ, b]) → Ε
  35. Segment(Δ, Ε) → t
  36. Rotate(Ε, 90°, Δ) → Ε'
  37. Polygon(Β, Ε', Γ) → t2, γ, β, ε'
  38. Segment(Ε', Δ) → c
  39. Midpoint(β) → Ζ
  40. Rotate(Β, α, Ζ) → Β'
  41. Rotate(Ε', α, Ζ) → Ε''
  42. Rotate(Γ, α, Ζ) → Γ'
  43. Polygon(Β', Ε'', Γ') → t2', γ', β', ε''
  44. Point(xAxis) → Η
  45. Point(Circle[Η, a]) → Θ
  46. Segment(Η, Θ) → d
  47. Point(d) → Ι
  48. Point(Circle[Ι, b]) → Κ
  49. Segment(Ι, Κ) → g_1
  50. Rotate(Κ, 90°, Ι) → Κ'
  51. Segment(Ι, Κ') → h_1
  52. OrthogonalLine(Κ', h_1) → i_1
  53. Point(i_1) → Λ
  54. Segment(Η, Κ') → j_1
  55. Segment(Κ', Λ) → k_1
  56. Segment(Λ, Θ) → l_1
  57. Segment(Θ, Η) → m_1
  58. Midpoint(l_1) → Μ
  59. Polygon(Η, Κ', Μ, Θ) → q2, η, κ', μ, θ
  60. Polygon(Κ', Λ, Μ) → t3, μ_1, n_1, λ
  61. Rotate(Κ', α, Μ) → Κ''
  62. Rotate(Λ, α, Μ) → Λ'
  63. Rotate(Μ, α, Μ) → Μ'
  64. Polygon(Κ'', Λ', Μ') → t3', μ', κ'', λ'