Area of Parallelogram by Alfred Estberg

GeoGebra Commands & Parameters

1. Segment(A, B) → base
2. Segment(A, C) → b
3. Circle(C, base) → c
4. Line(B, b) → d
5. Line(C, base) → e
6. Intersect(d, e) → D
7. Segment(B, D) → f
8. Segment(C, D) → g
9. Vector(A, C) → u
10. Sequence(A + (i * v), i, 1, Subdivisions) → list1
11. Sequence(B + (i * v), i, 1, Subdivisions) → list2
12. Sequence(Segment[Element[list1, i], Element[list2, i]], i, 1, Subdivisions) → list3
13. Vector(A, Intersect[OrthogonalLine[C, base], Line[A, base]]) → w
14. Sequence(Translate[Element[list3, p], Vector[((p * Translator) * (-h))]], p, 1, Subdivisions) → list4
15. Translate(C, Vector[(((-h) * Translator) * Subdivisions)]) → C'
16. Segment(A, C') → i
17. Translate(D, Vector[(((-h) * Translator) * Subdivisions)]) → D'
18. Segment(B, D') → j
19. Sequence(A + (i * v), i, 0, Subdivisions) → list5
20. Sequence(B + (i * v), i, 0, Subdivisions) → list6
21. Polygon(Element[list5, 1], Element[list5, 2], Element[list6, 2], Element[list6, 1]) → poly1, l, m, p, q
22. Sequence(Polygon[Element[list5, q], Element[list5, q + 1], Element[list6, q + 1], Element[list6, q]], q, 1, Subdivisions) → list7
23. Sequence(Translate[Element[list7, p], Vector[((p * Translator) * (-h))]], p, 1, Subdivisions) → list8
24. Line(A, base) → a
25. OrthogonalLine(D, a) → r
26. Intersect(a, r) → E
27. Segment(D, E) → height
28. Segment(A, E) → t
29. Angle(D, E, B) → α
30. Translate(D, Vector[E, B]) → D'_1
31. Translate(E, Vector[E, B]) → E'
32. Segment(D'_1, E') → height'
33. Segment(A, B) → s
34. Segment(B, D) → base_2
35. Intersect(OrthogonalLine[B, base_2], b) → F
36. Segment(B, F) → height_2
37. Polygon(A, F, B) → poly2, b_1, a_2, f_1
38. Translate(A, Vector[(o * Vector[B, D])]) → A'
39. Translate(F, Vector[(o * Vector[B, D])]) → F'
40. Translate(B, Vector[(o * Vector[B, D])]) → B'
41. Polygon(A', F', B') → poly2', b', a', f'
42. Segment(B', F') → height_2'
43. Polygon(B, F, F', D) → poly3, b_2, f_2, f'_1, d_1
44. Angle(D, B, F) → β