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Pentagonal Pyramid Net

Pentagonal Pyramid Net
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2012-04-27 00:13
PolygonSolid GeometryGeometric Construction
This example demonstrates the net of a pentagonal pyramid and its geometric properties. It involves core concepts like polygons, solid geometry, midpoints, distances, and vectors. The construction uses commands such as Segment, OrthogonalLine, Point, Intersect, Polygon, Midpoint, Perimeter, Distance, Vector, and Translate. Suitable for high school students learning solid geometry, helping them understand the unfolding and reconstruction of polyhedra.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Polygon(A, C, D, B) → poly1, PrismHeight, c_1, d_1, b_1
  8. Polygon(A, B, 5) → BaseArea, e, f, g, i, m, E, N, O
  9. Midpoint(D, C) → H
  10. OrthogonalLine(H, c_1) → h
  11. Point(h) → I
  12. Perimeter(BaseArea) → perimeterpoly2
  13. Midpoint(A, B) → J
  14. Distance(I, J) → distanceIJ
  15. Perimeter(BaseArea) → k
  16. LaTeX(PRISmVolume, true, true) → text2
  17. LaTeX(PyramidVolume, true, true) → text3
  18. LaTeX(PrismHeight, true, true) → text1
  19. Distance(B, A) → distanceBA
  20. Polygon(A, B, I) → poly2, BaseSideLength, a_1, b_3
  21. Circle(K, a) → p
  22. Perimeter(poly1) → perimeterpoly1
  23. Perimeter(poly1) → n
  24. Perimeter(poly1) → o
  25. Point(PrismHeight) → F
  26. Line(F, c_1) → j
  27. Intersect(j, d_1) → G
  28. Distance(G, F) → distanceGF
  29. Circle(K, distanceGF) → q
  30. Line(K, j) → l
  31. Intersect(q, l) → L, M
  32. Vector(K, L) → u
  33. Vector(K, M) → v
  34. Distance(A, B) → distanceAB
  35. LaTeX(BaseSideLength, true, true) → text5
  36. LaTeX(pyramidHeight, true, true) → text6
  37. Translate(A, u) → A'
  38. Translate(B, u) → B'
  39. Translate(I, u) → I'
  40. Polygon(A', B', I') → poly2', i', a', b'
  41. Translate(A', u) → A''
  42. Translate(B', u) → B''
  43. Translate(I', u) → I''
  44. Polygon(A'', B'', I'') → poly2'', i'', a'', b''
  45. Translate(A, v) → A'_1
  46. Translate(B, v) → B'_1
  47. Translate(I, v) → I'_1
  48. Polygon(A'_1, B'_1, I'_1) → poly2'_1, i'_1, a'_1, b'_1
  49. Translate(A'_1, v) → P
  50. Translate(B'_1, v) → Q
  51. Translate(I'_1, v) → R
  52. Polygon(P, Q, R) → poly3, r, p_1, q_1