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Cross Sections of a Trapezoidal Prism by nandrews (2)

Cross Sections of a Trapezoidal Prism by nandrews (2)
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2015-05-01 21:26
PolygonVectorSolid GeometryMatrixGeometric Construction
In collections Cross Sections of Prisms
This example demonstrates the various cross-sectional shapes formed by slicing through a trapezoidal prism at different angles. It involves core mathematical concepts like solid geometry, polygons, vectors, and matrix operations. Key GeoGebra commands and objects used in its construction include Intersect, Polygon, Prism, LaTeX, Point, OrthogonalLine, Plane, and IntersectPath. Suitable for high school students and math enthusiasts exploring spatial geometry and cross-section analysis.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Prism(poly1, 5.170266100867449) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  4. LaTeX(e, true, true) → text1
  5. Point(edgeFG) → I
  6. OrthogonalLine(I, b, space) → f
  7. OrthogonalLine(I, edgeEH, space) → g
  8. Intersect(edgeEH, g) → J
  9. Intersect(f, b) → K
  10. OrthogonalLine(J, d, space) → h
  11. Intersect(d, h) → L
  12. Polygon(I, J, L, K) → poly2, i, j, l, k
  13. Point(edgeCG) → M
  14. OrthogonalLine(M, edgeBF, space) → n
  15. Intersect(edgeBF, n) → N
  16. OrthogonalLine(N, edgeAE, space) → p
  17. Intersect(edgeAE, p) → O
  18. OrthogonalLine(O, edgeDH, space) → q
  19. Intersect(edgeDH, q) → P
  20. Polygon(M, N, O, P) → poly3, m_1, n_1, o, p_1
  21. Point(edgeCG) → Q
  22. OrthogonalLine(Q, edgeBF, space) → s
  23. Intersect(edgeBF, s) → R
  24. Point(edgeDH) → S
  25. Plane(R, Q, S) → t
  26. IntersectPath(t, e) → poly4, T, U, V, W, a_1, b_1, c_1, d_1
  27. Point(edgeGH) → Z
  28. Point(edgeFG) → A_1
  29. Point(edgeCG) → B_1
  30. Plane(Z, A_1, B_1) → v
  31. IntersectPath(v, e) → poly5, C_1, D_1, E_1, e_1, f_1, g_1