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Trapezium Area Calculation by Kathryn Peake (2)

Trapezium Area Calculation by Kathryn Peake (2)
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2017-10-05 19:22
PolygonVectorGeometric Construction
This example demonstrates the calculation of a trapezium's area. It involves core mathematical concepts such as trapezoid definition, area formula, and vector operations. GeoGebra commands and objects used in construction include Line, Point, Polygon, Midpoint, Rotate, OrthogonalLine, Intersect, Circle, Vector, and Translate. Suitable for middle school students and above to learn area calculation of geometric shapes, and to explore applications of vectors and transformations in geometry.

GeoGebra Commands & Parameters

  1. Line(C, B) → b
  2. Line(A, b) → c
  3. Point(c) → D
  4. Polygon(A, B, C, D) → poly1, a_1, b_1, c_1, d
  5. Midpoint(c_1) → E
  6. Rotate(A, α, E) → A'
  7. Rotate(B, α, E) → B'
  8. Rotate(C, α, E) → C'
  9. Rotate(D, α, E) → D'
  10. Polygon(A', B', C', D') → poly1', a', b', c', d'
  11. OrthogonalLine(A, b_1) → e
  12. Intersect(e, b_1) → F
  13. Circle(B, (a * (d + b_1))) → f
  14. Line(B, b_1) → g
  15. Intersect(f, g) → G, H
  16. Vector(B, F) → u
  17. Vector(F, A) → v
  18. Translate(H, u) → H'
  19. Vector(H, H') → w
  20. Translate(H', v) → H''
  21. Vector(H', H'') → h
  22. Polygon(H, H', H'') → poly2, h'', h_1, h'
  23. Polygon(A, F, C, D) → poly3, a_2, f_1, c_2, d_1
  24. Vector(A, F) → i
  25. Circle(A, 0.5) → k
  26. Intersect(k, e, 2) → I
  27. Circle(F, 0.5) → p
  28. Intersect(p, b) → J, K
  29. Vector(F, H') → j
  30. Vector(F, A) → l
  31. Translate(K, l) → K'
  32. Vector(K, K') → m
  33. Translate(I, j) → I'
  34. Vector(I, I') → n
  35. Vector(A, D) → s
  36. Translate(I, s) → I'_1
  37. Vector(I, I'_1) → t
  38. Line(B, i) → g_1
  39. Circle(B, 0.5) → k_1
  40. Intersect(k_1, g_1, 2) → L
  41. Vector(B, C) → u_1
  42. Translate(L, u_1) → L'
  43. Vector(L, L') → v_1
  44. Vector(I, I'_1) → r
  45. Vector(F, A) → w_1
  46. Vector(K', K) → q
  47. Vector(K, K') → j_1
  48. Vector(L, L') → i_1
  49. Vector(L', L) → l_1
  50. Vector(I'_1, I) → m_1
  51. Vector(I'_1, I') → e_1
  52. Vector(I', I'_1) → n_1