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Volume of a Parallelopiped

Volume of a Parallelopiped
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2017-06-05 05:09
VectorSolid GeometryGeometric Construction
This example demonstrates the calculation and visualization of the volume of a parallelepiped. It involves core mathematical concepts such as vectors, points, lines, faces, volume, distance, and angles. The construction utilizes GeoGebra commands and objects like Vector, Line, Intersect, Prism, Midpoint, Volume, Point, Distance, Segment, OrthogonalLine, Angle, and PointIn. It is suitable for high school solid geometry teaching or self-learning to understand the principles of volume calculation.

GeoGebra Commands & Parameters

  1. Vector(A, C) → u
  2. Vector(A, B) → v
  3. Vector(A, D) → w
  4. Line(D, v) → f
  5. Line(D, u) → g
  6. Line(B, w) → h
  7. Intersect(h, f) → E
  8. Line(E, g) → i
  9. Line(C, w) → j
  10. Intersect(g, j) → F
  11. Line(C, v) → k
  12. Line(B, u) → l
  13. Intersect(k, l) → G
  14. Line(F, k) → m
  15. Intersect(i, m) → H
  16. Vector(C, G) → a
  17. Vector(B, G) → b
  18. Vector(B, E) → c
  19. Vector(C, F) → d
  20. Vector(G, H) → e
  21. Vector(D, F) → n
  22. Vector(D, E) → p
  23. Vector(E, H) → q
  24. Vector(F, H) → r
  25. Prism(A, C, G, B, D) → o, I, edgeAC, edgeCG, edgeBG, edgeAB, edgeAD, edgeCI, edgeGJ, edgeBK, edgeDI, edgeIJ, J, edgeJK, edgeDK, K, faceABGC, faceACID, faceCGJI, faceBGJK, faceABKD, faceDIJK
  26. Midpoint(A, C) → L
  27. Midpoint(A, B) → M
  28. Midpoint(A, D) → N
  29. Volume(o) → volumeo
  30. Point(o) → Pointo
  31. Midpoint(A, P) → O
  32. Distance(P, A) → distancePA
  33. Segment(A, P) → t
  34. OrthogonalLine(D, t, space) → f_1
  35. Intersect(f_1, t) → Q
  36. Segment(D, Q) → g_1
  37. Angle(D, Q, A) → α
  38. Vector(A, Q) → u_1
  39. Midpoint(Q, A) → R
  40. Distance(A, Q) → distanceAQ
  41. Midpoint(A, Q) →
  42. Distance(A, Q) → a_1
  43. Midpoint(A, Q) →
  44. PointIn(faceABGC) → PointfaceABGC