Trapezium Area Demonstration by Mark Dabbs

GeoGebra Commands & Parameters

1. OrthogonalLine(A, a) → b
2. Point(b) → B
3. Line(C, b) → c
4. Point(c) → D
5. Segment(C, A) → d
6. Segment(B, D) → f
7. Segment(A, B) → g
8. Segment(C, D) → h
9. Midpoint(f) → E
10. Polygon(A, B, D, C) → poly1, a_1, b_1, d_1, c_1
11. Rotate(A, Rotate, E) → A'
12. Rotate(B, Rotate, E) → B'
13. Rotate(D, Rotate, E) → D'
14. Rotate(C, Rotate, E) → C'
15. Polygon(A', B', D', C') → poly1', a', b', d', c'
16. Midpoint(C, A) → F
17. Midpoint(B, D) → G
18. OrthogonalLine(F, h) → j
19. OrthogonalLine(G, h) → k
20. Intersect(k, h) → H
21. Intersect(j, h) → I
22. Intersect(k, g) → J
23. Intersect(j, g) → K
24. Line(C, D) → l
25. Line(A, B) → m
26. Intersect(j, l) → L
27. Intersect(k, m) → M
28. Intersect(j, m) → N
29. Intersect(k, l) → O
30. Point(k) → P
31. Polygon(P, O, D) → poly2, d_2, p, o
32. Point(j) → Q
33. Polygon(N, Q, A) → poly3, a_2, n, q
34. Polygon(B, P, M) → poly4, m_1, b_2, p_1
35. Polygon(Q, L, C) → poly5, c_2, q_1, l_1
36. Rotate(P, α, G) → P'
37. Rotate(O, α, G) → O'
38. Rotate(D, α, G) → D'_1
39. Polygon(P', O', D'_1) → poly2', d'_1, p', o'
40. Rotate(N, α, F) → N'
41. Rotate(Q, α, F) → Q'
42. Rotate(A, α, F) → A'_1
43. Polygon(N', Q', A'_1) → poly3', a'_1, n', q'
44. Rotate(B, (-α), G) → B'_1
45. Rotate(P, (-α), G) → P'_1
46. Rotate(M, (-α), G) → M'
47. Polygon(B'_1, P'_1, M') → poly4', m', b'_1, p'_1
48. Rotate(Q, (-α), F) → Q'_1
49. Rotate(L, (-α), F) → L'
50. Rotate(C, (-α), F) → C'_1
51. Polygon(Q'_1, L', C'_1) → poly5', c'_1, q'_1, l'
52. If(x(A) > x(C), If[x(B) < x(D), Polygon[A, B, G, O, L, F], Polygon[A, M, G, D, L, F]], If[x(B) < x(D), Polygon[N, B, G, O, C, F], Polygon[N, M, G, D, C, F]]) → polyHex
53. If(x(A) > x(C), If[x(B) < x(D), Polygon[A, B, G, O, L, F], Polygon[A, M, G, D, L, F]], If[x(B) < x(D), Polygon[N, B, G, O, C, F], Polygon[N, M, G, D, C, F]]) → polyHexBorder
54. Midpoint(B, D) → R
55. Line(A, R) → s
56. Line(C, D) → t
57. Intersect(t, s) → S
58. Polygon(A, B, R) → poly6, r_1, a_3, b_3
59. Rotate(A, (-β), R) → A'_2
60. Rotate(B, (-β), R) → B'_2
61. Rotate(R, (-β), R) → R'
62. Polygon(A'_2, B'_2, R') → poly6', r', a'_2, b'_2
63. Polygon(A, C, D, R) → poly7, a_4, c_3, d_3, r_2
64. Polygon(A, R, D, C) → poly8, a_5, r_3, d_4, c_4
65. Polygon(A'_2, B'_2, R) → poly9, r_4, a'_3, b'_3
66. Segment(F, G) → e_1
67. Polygon(F, G, B, A) → poly10, f_1, g_1, b_4, a_6
68. Rotate(F, (-γ), G) → F'
69. Rotate(G, (-γ), G) → G'
70. Rotate(B, (-γ), G) → B'_3
71. Rotate(A, (-γ), G) → A'_3
72. Polygon(F', G', B'_3, A'_3) → poly10', f', g', b'_4, a'_4
73. Polygon(C, F, G, D) → poly11, c_5, f_2, g_2, d_5
74. Midpoint(Bt, Dt) → T
75. Polygon(A, D, B) → poly12, b_5, a_7, d_6
76. Rotate(A, (-δ), T) → A'_4
77. Rotate(D, (-δ), T) → D'_2
78. Rotate(B, (-δ), T) → B'_4
79. Polygon(A'_4, D'_2, B'_4) → poly12', b'_5, a'_5, d'_2
80. Segment(A, D) → h_1
81. Segment(A, D) → i_1
82. Polygon(A, C, D) → poly13, d_7, a_8, c_6
83. Segment(Ah, Dh) → j_1
84. OrthogonalLine(Ah, c) → k_1
85. OrthogonalLine(Dh, c) → n_1
86. Point(k_1) → V
87. Point(n_1) → W
88. OrthogonalLine(V, c) → t_1
89. OrthogonalLine(W, c) → e_2
90. Intersect(t_1, c) → Z
91. Intersect(e_2, c) → A_1
92. Segment(A_1, Z) → s_1