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Area and Perimeter Relationship Demo

Area and Perimeter Relationship Demo
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2015-04-18 21:10
TrianglePolygonCoordinate GeometryGeometric Construction
This example demonstrates the calculation and relationship between area and perimeter of shapes like triangles and polygons; core math concepts include area, perimeter, and coordinate geometry; constructed using GeoGebra commands such as Line, Point, Segment, Polygon, Distance, Perimeter; suitable for high school mathematics teaching and learning to understand basic geometric properties.

GeoGebra Commands & Parameters

  1. Line((0, 0), (0, 1)) → yaxis
  2. Point(yaxis) → A_1
  3. OrthogonalLine(A_1, yAxis) → a
  4. Point(a) → B_1
  5. Segment(A_1, B_1) → b
  6. Point(b) → C_1
  7. Point(b) → D_1
  8. Segment(A_1, C_1) → c
  9. Segment(C_1, D_1) → d
  10. Segment(D_1, B_1) → e
  11. Vector(A_1, C_1) → u
  12. Translate(A, u) → C
  13. Segment(A, C) → f
  14. Circle(A, d) → g
  15. Circle(C, e) → h
  16. Intersect(g, h, 1) → B
  17. Polygon(A, B, C) → poly1, e', e_1, f_1
  18. Distance(e', e_1) → i
  19. Distance(c, f) → j
  20. Distance(e, d) → k
  21. OrthogonalLine(A_1, c) → l
  22. OrthogonalLine(B_1, e) → m
  23. Point(yaxis) → E_1
  24. OrthogonalLine(E_1, l) → n
  25. Intersect(m, n) → F_1
  26. Segment(E_1, F_1) → p
  27. Point(p) → G
  28. Point(p) → H
  29. Segment(E_1, G) → q
  30. Segment(G, H) → r
  31. Segment(H, F_1) → s
  32. Vector(E_1, G) → v
  33. Translate(D, v) → F
  34. Circle(D, r) → t
  35. Circle(F, s) → c_1
  36. Intersect(t, c_1, 1) → E
  37. Polygon(D, E, F) → poly2, i', i_1, j_1
  38. Segment(E_1, G) → a_1
  39. Perimeter(poly1) → perimeterpoly1
  40. Perimeter(poly2) → perimeterpoly2
  41. Distance(a_1, r) → o
  42. Distance(s, e) → w
  43. Distance(d, c) → z

AI Drawing Prompt Reference

Draw a triangle ABC and a triangle DEF, where triangle ABC is formed by points A, B, and C, with point A on the y-axis and B and C obtained by translating A along vector u; triangle DEF is formed by points D, E, and F, with D, E, and F obtained by translating D along vector v. Calculate the perimeters of both triangles.
The prompt above was compiled from the original drawing commands and is for reference only.