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Parallelogram Area Demonstration by Mark Dabbs

Parallelogram Area Demonstration by Mark Dabbs
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2014-09-22 23:24
PolygonTrigonometryCoordinate GeometryIntegralGeometric Construction
This example visually demonstrates the calculation of a parallelogram's area by showing the base times height. Core math concepts include parallelograms, area formulas, similar triangles, and coordinate geometry. Construction involves GeoGebra commands like Point, OrthogonalLine, Segment, Line, Intersect, Polygon, Dilate, Circle, and objects such as Translate, g, A, a, C, B_1, b, c, d, D_1, e, f, h, i, j, B, D, k, E, l, m, n, F, p, poly1, a_1, e_1, f_1, d_1, poly2, e_2, c_1, b_1, f_2, q, r, s, C', t, g_1. Suitable for middle school students and above learning parallelogram area formulas and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(g) → A
  2. OrthogonalLine(A, g) → a
  3. Point(g) → C
  4. Segment(C, B_1) → b
  5. Line(A, b) → c
  6. Line(B_1, g) → d
  7. Intersect(c, d) → D_1
  8. Segment(D_1, B_1) → e
  9. Segment(A, D_1) → f
  10. OrthogonalLine(C, g) → h
  11. OrthogonalLine(D_1, g) → i
  12. OrthogonalLine(B_1, g) → j
  13. Intersect(g, i) → B
  14. Intersect(g, j) → D
  15. Segment(If[x(B) ≥ x(A), B, A], If[x(B) ≥ x(A), C, D]) → k
  16. Point(k) → E
  17. Segment(A, B) → l
  18. Segment(C, D) → m
  19. OrthogonalLine(E, e) → n
  20. Intersect(n, e) → F
  21. Segment(F, E) → p
  22. Polygon(A, E, F, D_1) → poly1, a_1, e_1, f_1, d_1
  23. Polygon(E, C, B_1, F) → poly2, e_2, c_1, b_1, f_2
  24. Segment(B_1, F) → q
  25. Segment(F, D_1) → r
  26. Segment(A, C) → s
  27. Dilate(C, Translate, A) → C'
  28. Line(C', b) → t
  29. Line(B_1, s) → g_1
  30. Intersect(t, g_1) → G
  31. Circle(G, Segment[D_1, F]) → h_1
  32. Circle(C', Segment[A, E]) → k_1
  33. Line(A, C) → i_1
  34. Intersect(k_1, i_1) → H, I
  35. Intersect(h_1, g_1) → J, K
  36. Segment(B_1, K) → j_1
  37. Segment(K, I) → l_1
  38. Segment(I, C') → m_1
  39. Segment(G, C') → n_1
  40. Polygon(C', G, K, I) → poly3, c', g_2, k_2, i_2
  41. Segment(E, C) → p_1
  42. Segment(G, F) → q_1
  43. Segment(F, E) → r_1
  44. Segment(I, K) → s_1