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Volume of a Triangular Prism by MrVisconti

Volume of a Triangular Prism by MrVisconti
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2020-05-19 10:33
VectorCoordinate GeometrySolid GeometryMatrixGeometric Construction
This example demonstrates how to calculate the volume of a triangular prism using GeoGebra, involving core concepts like volume formulas, 3D vectors, coordinate geometry, and matrix operations. Key GeoGebra commands and objects used include Dilate, Vector, Circle, Line, Intersect, Translate, Midpoint, Polygon, Segment, If, and AngularBisector. Suitable for high school students and educators for learning and teaching purposes.

GeoGebra Commands & Parameters

  1. Dilate(F, Height, E) → G
  2. Vector(E, G) → u
  3. Dilate(I, base, H) → L
  4. Vector(H, L) → v
  5. Circle(J, height) → g
  6. Line(J, K) → h
  7. Intersect(g, h, 1) → M
  8. Vector(J, M) → w
  9. Translate(A, v) → B
  10. Circle(J, 1) → d
  11. Midpoint(A, B) → C
  12. Midpoint(C, A) → D
  13. Translate(D, Vector[w / 2]) → N
  14. Polygon(A, N, B) → P, b, a, n
  15. Translate(A, u) → A'
  16. Translate(N, u) → N'
  17. Translate(B, u) → B'
  18. Polygon(A', N', B') → P', b', a', n'
  19. Polygon(A', N', N, A) → Q, a'_1, n'_1, n_1, a_1
  20. Polygon(N', N, B, B') → R, n'_2, n_2, b_1, b'_1
  21. Polygon(B', B, A, A') → S, b'_2, b_2, a_2, a'_2
  22. Segment(N, D) → c
  23. Midpoint(A, A') → O
  24. Midpoint(N, D) → T
  25. If(VolumeFormula ≟ 1, U) → Z
  26. If(VolumeSolution ≟ 1, V) → A_1
  27. AngularBisector(A, N, B) → e
  28. AngularBisector(B, A, N) → f
  29. Intersect(f, e) → W
  30. Translate(W, u) → Y

AI Drawing Prompt Reference

Draw a triangular prism by first creating the triangular base, then generating the two bases through translation and rotation. Connect corresponding vertices to form the prism's sides, and finally calculate and display the prism's volume.
The prompt above was compiled from the original drawing commands and is for reference only.