MathPlotAI Logo MathPlotAI

Cross Section of a Rectangular Pyramid

Cross Section of a Rectangular Pyramid
Loading the math board and drawing, please wait…
2020-03-04 21:51
PolygonSolid GeometryGeometric Construction
In collections Cross Sections
This GeoGebra example demonstrates the cross-section of a rectangular pyramid when intersected by a plane, showing how a 3D solid is cut to produce a 2D polygon. Core mathematical concepts include solid geometry, pyramids, cross-sections, plane-polyhedron intersections, and spatial reasoning. The construction uses commands such as Polygon, Pyramid, Point, Plane, Intersect, IntersectPath, OrthogonalLine, and OrthogonalPlane to define the pyramid, the cutting plane, and compute the intersection edges. It is suitable for high school or early college students learning about 3D visualization, section shapes, and geometric construction in dynamic mathematics software.

GeoGebra Commands & Parameters

  1. Polygon(U, P, Q, W) → t1, m, n, q, r
  2. Pyramid(t1, o) → ThePyra, S, facePSU, facePQS, faceQSW, faceSUW, edgeSU, edgePS, edgeQS, edgeSW
  3. Point(xAxis) → V
  4. Point(xAxis) → A
  5. Point(zAxis) → O
  6. Point(xAxis) → K
  7. Point(yAxis) → J
  8. Point(xAxis) → I
  9. Plane(I, K, O) → b
  10. Plane(I, J, K) → p
  11. PointIn(b) → CenterOfNormalAngle
  12. Circle(CenterOfNormalAngle, 0.25, b) → d
  13. Line(CenterOfNormalAngle, xAxis) → g
  14. Point(yAxis) → B
  15. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  16. Intersect(xAxis, yAxis) → M
  17. OrthogonalLine(CenterOfNormalAngle, g, b) → h
  18. Intersect(g, d) → i_1, i_2
  19. CircleArc(CenterOfNormalAngle, i_1, i_2, b) → ArcForPlaneAngle
  20. Point(ArcForPlaneAngle) → NormalAngleHandle
  21. Segment(CenterOfNormalAngle, NormalAngleHandle) → NormalSeg
  22. PointIn(ThePyra) → SliceChooser
  23. OrthogonalPlane(SliceChooser, NormalSeg) → PerPenPlane
  24. PointIn(PerPenPlane) → N
  25. IntersectPath(PerPenPlane, ThePyra) → poly1, D, E, F, G, f, i, j, k

AI Drawing Prompt Reference

Draw a right rectangular pyramid and then cut it with a plane to show the 2D polygon formed by the cut. First, draw a rectangular base, then construct the pyramid, and finally compute and display the edges of the cut.
The prompt above was compiled from the original drawing commands and is for reference only.