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Volume of a Tetrahedron

Volume of a Tetrahedron
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2014-10-13 18:02
Solid GeometryTransformation
This example demonstrates the relationship between the volume of a prism and a pyramid. By constructing a prism and a pyramid, students can intuitively understand the concept of volume ratio. Commands used include Vector, Segment, Polygon, Translate, suitable for students in middle school and above studying solid geometry.

GeoGebra Commands & Parameters

  1. Vector(E, F) → u
  2. Segment(A, B) → a
  3. Segment(B, C) → b
  4. Segment(A, C) → c
  5. Polygon(A, C, B) → poly1, b_1, a_1, c_1
  6. Translate(A, u) → A'
  7. Translate(C, u) → C'
  8. Translate(B, u) → B'
  9. Polygon(A', C', B') → poly1', b', a', c'
  10. Segment(A, A') → d
  11. Segment(B, B') → e
  12. Segment(C, C') → f
  13. Segment(A', B) → g
  14. Segment(A', C) → h
  15. Segment(B', C) → i
  16. Polygon(A', A, B) → poly2, b_2, a'_1, a_2
  17. Polygon(A', B, C) → poly3, c_2, a'_2, b_3
  18. Polygon(A', C', C) → poly4, c_3, a'_3, c'_1
  19. Polygon(B', A', C) → poly5, c_4, b'_1, a'_4
  20. Polygon(B', C', C) → poly6, c_5, b'_2, c'_2
  21. Polygon(B, B', C) → poly7, c_6, b_4, b'_3
  22. Polygon(A', B', B) → poly8, b_5, a'_5, b'_4

AI Drawing Prompt Reference

Draw a tetrahedron to demonstrate the concept of volume ratio by constructing a prism and a pyramid. First, draw triangle ABC, then use vector translation to get A', B', and C'. Next, draw the two base polygons and the side polygons of the tetrahedron.
The prompt above was compiled from the original drawing commands and is for reference only.