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Calculating Area of a Parallelogram by Lee W Fisher

Calculating Area of a Parallelogram by Lee W Fisher
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2017-12-20 16:00
PolygonTrigonometryGeometric Construction
This example demonstrates how to calculate the area of a parallelogram by constructing it and dividing it into triangles. Key math concepts include parallelogram properties, triangle area formula, and geometric transformations. GeoGebra commands used in construction are Polygon, Point, Segment, Midpoint, Circle, Rotate, Angle, Ray, Intersect, OrthogonalLine, and Line. Suitable for middle school students and above learning the parallelogram area formula and geometric constructions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Point(Circle[I, sqrt(45)]) → J
  3. Segment(I, J) → i
  4. Midpoint(I, J) → K
  5. Circle(K, J) → k
  6. Rotate(J, atan(2), I) → J'
  7. Angle(J, I, J') → α
  8. Ray(I, J') → j
  9. Intersect(k, j, 2) → L
  10. Polygon(I, L, J) → t1, j_1, i_1, l
  11. Point(Circle[M, 6]) → N
  12. Segment(M, N) → n
  13. Circle(M, 7) → p
  14. OrthogonalLine(M, n) → q
  15. OrthogonalLine(N, n) → r
  16. Intersect(p, q, 2) → O
  17. OrthogonalLine(O, q) → s
  18. Intersect(r, s) → P
  19. Rotate(P, atan(0.5), O) → P'
  20. Angle(P, O, P') → β
  21. Ray(O, P') → t
  22. Intersect(r, t) → Q
  23. Polygon(M, N, Q, O) → q3, m_1, n_1, q_1, o
  24. Angle(Q, N, M) → γ
  25. Point(Circle[E, 6]) → F
  26. Segment(E, F) → f
  27. OrthogonalLine(E, f) → g
  28. OrthogonalLine(F, f) → h
  29. Point(h) → G
  30. Point(Circle[G, 10]) → H
  31. Segment(G, H) → f_1
  32. Point(g) → R
  33. Point(Circle[R, 10]) → S
  34. Segment(R, S) → g_1
  35. Polygon(G, R, S, H) → q2, g_2, r_1, s_1, h_1
  36. Angle(r_1, f) → δ
  37. Point(Circle[H_1, sqrt(116)]) → I_1
  38. Segment(H_1, I_1) → l_1
  39. Midpoint(H_1, I_1) → J_1
  40. Circle(J_1, I_1) → p_1
  41. Rotate(H_1, atan(2.5), I_1) → T
  42. Angle(H_1, I_1, T) → ε
  43. Ray(I_1, T) → t_1
  44. Intersect(p_1, t_1, 2) → U
  45. Polygon(H_1, I_1, U) → t2, u_1, h_2, i_2
  46. Point(Circle[V, 4]) → P_1
  47. Segment(V, P_1) → m_2
  48. Circle(P_1, sqrt(29)) → d_2
  49. Circle(V, sqrt(29)) → e_2
  50. Intersect(d_2, e_2, 1) → Q_1
  51. Line(Q_1, m_2) → n_2
  52. Segment(V, Q_1) → p_2
  53. Line(P_1, p_2) → q_2
  54. Intersect(n_2, q_2) → R_1
  55. Polygon(V, P_1, R_1, Q_1) → q5, v, p_3, r_2, q_3
  56. Point(Circle[S_1, 5]) → T_1
  57. Segment(S_1, T_1) → s_2
  58. OrthogonalLine(S_1, s_2) → t_2
  59. OrthogonalLine(T_1, s_2) → a_2
  60. Circle(S_1, 4) → c_3
  61. Intersect(c_3, t_2, 1) → U_1
  62. Circle(T_1, 2) → d_3
  63. Intersect(d_3, a_2, 1) → V_1
  64. Polygon(U_1, V_1, T_1, S_1) → q6, u_2, v_1, t_3, s_3
  65. Point(Circle[W, sqrt(29)]) → Z
  66. Segment(W, Z) → k_1
  67. Midpoint(W, Z) → A_1
  68. Circle(A_1, Z) → c_1
  69. Rotate(W, atan(2.5), Z) → W'
  70. Angle(W, Z, W') → ζ
  71. Ray(Z, W') → b_1
  72. Intersect(c_1, b_1, 2) → B_1
  73. Polygon(Z, B_1, W) → t3, w_1, z_1, b_2

AI Drawing Prompt Reference

Draw a parallelogram and divide it into two triangles. Start by creating four points A, B, C, and D, then use these points to create a parallelogram. Next, draw a circle with point C as the center and find point J on the circle. Connect I and J. Then, find the midpoint K of I and J, and draw a circle with K as the center. Rotate J around I by atan(2) to get J', and find the angle α between IJ'. Draw a ray from I to J', and find the second intersection point L with the circle K. Use I, L, and J to create a triangle. Continue drawing circles, rotating, and finding new intersection points and angles until the entire figure is completed.
The prompt above was compiled from the original drawing commands and is for reference only.