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Volume of a Parallelepiped

Volume of a Parallelepiped
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2017-04-25 20:54
VectorCoordinate GeometrySolid Geometry
This example demonstrates how to calculate the volume of a parallelepiped using geometric construction. Key mathematical concepts include vectors, solid geometry, and coordinate geometry. Using GeoGebra commands such as Vector, Point, Segment, and Intersect, the construction process of a parallelepiped is visually illustrated. Suitable for high school mathematics education and students learning solid geometry.

GeoGebra Commands & Parameters

  1. Vector(O, B) → u
  2. Vector(O, A) → v
  3. Vector(O, C) → w
  4. Segment(A, D) → f
  5. Segment(B, D) → g
  6. Segment(D, E) → h
  7. Segment(C, F) → i
  8. Segment(C, G) → j
  9. Segment(G, E) → k
  10. Segment(B, G) → l
  11. Segment(F, A) → m
  12. Segment(F, E) → n
  13. Angle(B, O, A) → α
  14. Vector(O, O + v ⊗ u) → a
  15. Segment(O, H) → p
  16. OrthogonalLine(C, p, space) → q
  17. Point(q) → I
  18. Vector(O, I) → b
  19. Segment(C, I) → r
  20. Midpoint(O, I) → J
  21. Midpoint(O, H) → K
  22. Segment(O, B) → s
  23. OrthogonalLine(A, s, space) → t
  24. Intersect(s, t) → L
  25. Segment(A, L) → c
  26. Angle(O, L, A) → β