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Shape Fitting Puzzle

Shape Fitting Puzzle
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2019-03-05 05:55
Polygon
In collections Surface Area
This is a puzzle to fit shapes with equivalent areas. The example involves concepts such as area, trapezoid, and tangent line. It is constructed using GeoGebra commands such as Intersect, Polygon, Point, Segment, Midpoint, LineBisector, Circle, Line, and OrthogonalLine. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  3. Point(Circle[F, Distance[A, B]]) → G
  4. Segment(F, G) → k
  5. Midpoint(k) → H
  6. Midpoint(f) → I
  7. LineBisector(k) → l
  8. Circle(H, Distance[I, D]) → c
  9. Intersect(c, l, 2) → J
  10. Polygon(F, J, G) → t1, g_1, f_1, j_1
  11. Segment(D, B) → m
  12. Line(C, m) → n
  13. Line(D, xAxis) → p
  14. Intersect(n, p) → K
  15. Midpoint(h) → L
  16. Point(Circle[M, Distance[D, C]]) → N
  17. Segment(M, N) → q
  18. Midpoint(q) → O
  19. OrthogonalLine(O, q) → r
  20. Circle(O, Distance[L, K]) → d
  21. Intersect(d, r, 2) → P
  22. Polygon(M, P, N) → t2, n_1, m_1, p_1
  23. Intersect(n, xAxis) → Q
  24. Point(Circle[R, Distance[B, Q]]) → S
  25. Segment(R, S) → s
  26. Midpoint(B, Q) → T
  27. Midpoint(s) → U
  28. OrthogonalLine(U, s) → t
  29. Circle(U, Distance[T, C]) → e
  30. Intersect(e, t) → V, W
  31. Polygon(R, W, S) → t3, s_1, r_1, w
  32. Point(xAxis) → Z
  33. Circle(Z, Distance[A, Q]) → c_1
  34. Intersect(c_1, xAxis, 2) → A_1
  35. Line(A_1, n) → a
  36. Segment(D, A) → b
  37. Line(Z, b) → h_1
  38. Point(Circle[B_1, Distance[D, B]]) → C_1
  39. Segment(B_1, C_1) → i_1
  40. Midpoint(m) → D_1
  41. Segment(D_1, C) → k_1
  42. Midpoint(i_1) → E_1
  43. OrthogonalLine(E_1, i_1) → l_1
  44. Circle(E_1, k_1) → d_1
  45. Intersect(d_1, l_1, 2) → F_1
  46. Polygon(B_1, F_1, C_1) → t4, c_2, b_1, f_2
  47. Intersect(p, h_1) → G_1
  48. Intersect(p, a) → H_1
  49. Polygon(Z, G_1, H_1, A_1) → q1, z_1, g_2, h_2, a_1

AI Drawing Prompt Reference

Draw a shape composed of multiple trapezoids and triangles, with one large trapezoid and four smaller ones, each having the same area. Start by drawing the coordinate axes, then draw a large trapezoid in the first quadrant. Next, draw four smaller trapezoids inside the large one, ensuring each smaller trapezoid has the same area as the large one. Finally, connect the relevant points and segments to form the complete shape.
The prompt above was compiled from the original drawing commands and is for reference only.