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Rectangular Pyramid by Mathguru

Rectangular Pyramid by Mathguru
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2012-11-03 12:46
PolygonSolid GeometryCalculusTransformationGeometric Construction
In collections SA and Volume
This example demonstrates a rectangular pyramid, a three‑dimensional solid with a rectangular base, constructed using GeoGebra. It involves core concepts from solid geometry, coordinate geometry, transformations (dilation, translation), and differential calculus. The construction uses commands such as Dilate, Vector, Circle, Line, Intersect, Translate, Midpoint, Polygon, Segment, and If, with objects representing height, length, width, and other parameters. It is suitable for high‑school or early university students learning geometric modeling and spatial visualization.

GeoGebra Commands & Parameters

  1. Dilate(F, height, E) → G
  2. Vector(E, G) → u
  3. Dilate(I, length, H) → L
  4. Vector(H, L) → v
  5. Circle(J, width) → g
  6. Line(J, K) → h
  7. Intersect(g, h, 1) → M
  8. Vector(J, M) → w
  9. Translate(A, v) → B
  10. Translate(A, Vector[w / 2]) → C
  11. Translate(C, v) → D
  12. Midpoint(C, B) → N
  13. Translate(N, u) → O
  14. Polygon(A, B, D, C) → P, a, b, d, c
  15. Polygon(O, C, D) → Q, d_1, o, c_1
  16. Polygon(O, A, C) → R, c_2, o_1, a_1
  17. Polygon(O, D, B) → S, b_1, o_2, d_2
  18. Polygon(O, A, B) → T, b_2, o_3, a_2
  19. Midpoint(B, D) → U
  20. Segment(O, N) → e
  21. Segment(O, U) → f
  22. Midpoint(O, U) → W
  23. Midpoint(O, N) → V
  24. Midpoint(A, B) → Y
  25. If(height ≤ 5, C) → Z
  26. Segment(Z, O) → i
  27. Segment(Z, A) → j
  28. If(VolumeFormula ≟ 1, A_1) → E_1
  29. If(SurfaceAreaFormula ≟ 1, C_1) → G_1
  30. If(VolumeSolution ≟ 1, B_1) → F_1
  31. If(SurfaceAreaSolution ≟ 1, D_1) → H_1

AI Drawing Prompt Reference

Create a rectangular pyramid by first drawing a rectangle to serve as the base, indicating its length and width. From each corner of the base, draw line segments up to a common apex point positioned above the base at a height. Mark the apex, the base center, and the midpoints of the base edges. Include lines from the apex to the base center and to the midpoints of the base edges. Optionally, add a cross‑section plane that cuts through the pyramid to reveal internal geometry, such as a triangular face or a slice showing the height and base dimensions.
The prompt above was compiled from the original drawing commands and is for reference only.