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Calculating Parallelogram Area by Daniel Mentrard

Calculating Parallelogram Area by Daniel Mentrard
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2020-12-08 00:59
PolygonVectorCoordinate Geometry
This example demonstrates how to calculate the area of a parallelogram using vector cross product and base times height. Key math concepts include vectors, vector cross product, polygon construction, and coordinate geometry. It constructs the parallelogram and auxiliary segments using commands like Intersect, Vector, Translate, Polygon, Segment, Centroid, and Midpoint, making it suitable for high school mathematics teaching and student learning of spatial vector applications.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Vector(O, A) → u
  3. Vector(O, B) → v
  4. Translate(A, v) → P
  5. Polygon(O, A, P, B) → poly1, o, a, p, b
  6. Polygon(O, C, A) → poly2, a_1, o_1, c
  7. Polygon(H, B, P) → poly3, p_1, h, b_1
  8. Polygon(P, A, E) → poly4, e, p_2, a_2
  9. Polygon(F, B, O) → poly5, o_2, f, b_2
  10. Polygon(A, C, D, E) → poly6, a_3, c_1, d, e_1
  11. Polygon(F, B, H, G) → poly7, f_1, b_3, h_1, g
  12. Segment(B, P) → i
  13. Segment(P, A) → j
  14. Segment(A, E) → k
  15. Segment(E, P) → l
  16. Segment(D, E) → m
  17. Segment(A, C) → n
  18. Segment(H, P) → q
  19. Segment(H, B) → r
  20. Segment(B, F) → s
  21. Segment(G, H) → t
  22. Centroid(poly2) → I
  23. Centroid(poly1) → J
  24. Centroid(poly3) → K
  25. Centroid(poly4) → L
  26. Centroid(poly5) → M
  27. Centroid(poly6) → N
  28. Centroid(poly7) → Q
  29. Midpoint(Z, B_1) → F_1
  30. Midpoint(Z, A_1) → G_1
  31. Midpoint(W, V) → H_1
  32. Midpoint(V, U) → I_1
  33. Midpoint(R, S) → J_1
  34. Midpoint(S, T) → K_1
  35. Midpoint(D_1, E_1) → L_1
  36. Midpoint(E_1, C_1) → M_1
  37. Vector(F_1, B_1) → w
  38. Vector(F_1, Z) → u_1
  39. Vector(G_1, Z) → v_1
  40. Vector(G_1, A_1) → w_1
  41. Vector(H_1, W) → d_1
  42. Vector(H_1, V) → g_1
  43. Vector(I_1, V) → i_1
  44. Vector(I_1, U) → j_1
  45. Vector(J_1, S) → k_1
  46. Vector(J_1, R) → l_1
  47. Vector(K_1, S) → m_1
  48. Vector(K_1, T) → n_1
  49. Vector(L_1, E_1) → q_1
  50. Vector(L_1, D_1) → r_1
  51. Vector(M_1, C_1) → s_1
  52. Vector(M_1, E_1) → t_1

AI Drawing Prompt Reference

Draw a parallelogram formed by two vectors originating from a common point, with the fourth vertex determined by the vector sum. Construct several auxiliary triangles and quadrilaterals inside and around the parallelogram, using vertices, points on edges, and additional points, creating a grid-like pattern. Include the diagonals of the parallelogram and the sides of all auxiliary shapes. Mark the centroids of each polygonal region and the midpoints of selected segments. The overall figure illustrates vector operations and area decomposition in a coordinate plane.
The prompt above was compiled from the original drawing commands and is for reference only.