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Cross Sections of a Square Based Pyramid

Cross Sections of a Square Based Pyramid
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2016-07-20 23:06
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the cross sections of a square based pyramid. Key mathematical concepts include the properties of sections in solid geometry. Using GeoGebra commands such as Intersect, Point, Polygon, etc., various faces and sections of the pyramid can be constructed. Suitable for high school geometry education or self-study.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Pyramid(poly1, 6) → e, E, faceABE, faceBCE, faceCDE, faceADE, edgeAE, edgeBE, edgeCE, edgeDE
  5. Point(edgeBE) → F
  6. Line(F, b) → f
  7. Intersect(f, edgeCE) → G
  8. OrthogonalLine(F, a, space) → g
  9. OrthogonalLine(G, c, space) → h
  10. Intersect(a, g) → H
  11. Intersect(c, h) → I
  12. Point(edgeBE) → J
  13. OrthogonalPlane(J, edgeBE) → k
  14. IntersectPath(k, e) → poly3, K, q, L, M, N, O, l, m, n, p
  15. Point(edgeCE) → P
  16. Line(P, b) → i
  17. Intersect(i, edgeBE) → Q
  18. Line(P, c) → r
  19. Intersect(edgeDE, r) → R
  20. Plane(Q, P, R) → s
  21. IntersectPath(s, e) → poly2, S, T, U, V, t, a_1, b_1, c_1
  22. OrthogonalLine(F, poly1) → d_1
  23. Intersect(edgeBE, b) → W
  24. Intersect(edgeDE, c) → Z
  25. Segment(W, Z) → e_1
  26. Intersect(e_1, d_1) → A_1
  27. OrthogonalLine(F, e_1, space) → f_1
  28. OrthogonalPlane(F, e_1) → v
  29. IntersectPath(v, e) → poly4, B_1, C_1, D_1, g_1, h_1, i_1
  30. Point(edgeBE) → E_1
  31. Line(E_1, b) → j_1
  32. Intersect(edgeCE, j_1) → F_1
  33. OrthogonalLine(F_1, poly1) → k_1
  34. Point(k_1) → G_1
  35. Plane(E_1, F_1, G_1) → w
  36. IntersectPath(w, e) → poly5, H_1, I_1, J_1, K_1, l_1, m_1, n_1, p_1