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Cross Sections of a Rectangular Prism

Cross Sections of a Rectangular Prism
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2016-05-10 20:54
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the cross sections of a rectangular prism. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Intersect, Point, and Polygon, the construction of the prism and its cross sections is illustrated. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → D
  3. Polygon(A, B, C, D) → poly1, a, b, c, d
  4. Prism(poly1, 2.975831365655143) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  5. Point(edgeGH) → I
  6. OrthogonalLine(I, c, space) → f
  7. Intersect(c, f) → J
  8. OrthogonalLine(I, edgeEF, space) → g
  9. Intersect(edgeEF, g) → K
  10. OrthogonalLine(K, a, space) → h
  11. Plane(I, J, K) → i
  12. IntersectPath(i, e) → poly2, L, M, N, O, j, k, l, m
  13. Point(edgeCG) → P
  14. OrthogonalLine(P, edgeBF, space) → p
  15. OrthogonalLine(P, edgeDH, space) → q
  16. Intersect(edgeBF, p) → Q
  17. Intersect(edgeDH, q) → R
  18. Plane(Q, P, R) → o
  19. IntersectPath(o, e) → poly3, S, T, U, V, r, s, t, a_1
  20. Point(edgeCG) → W
  21. OrthogonalLine(W, edgeBF, space) → b_1
  22. Point(edgeDH) → Z
  23. Intersect(edgeBF, b_1) → A_1
  24. Plane(A_1, W, Z) → v
  25. IntersectPath(v, e) → poly4, B_1, C_1, D_1, E_1, c_1, d_1, e_1, f_1
  26. Point(edgeEF) → F_1
  27. Point(edgeFG) → G_1
  28. Point(edgeBF) → H_1
  29. Plane(F_1, G_1, H_1) → g_1
  30. IntersectPath(g_1, e) → poly5, I_1, J_1, K_1, N_1, h_1, i_1, j_1, l_1
  31. IntersectPath(g_1, faceEFGH) → k_1
  32. Intersect(g_1, faceEFGH) → L_1, M_1