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Volume of Triangular Pyramid

Volume of Triangular Pyramid
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2020-07-07 09:33
Solid GeometryGeometric Construction
In collections Mensuration
This example demonstrates the calculation of the volume of a triangular pyramid. Key mathematical concepts include the volume calculation in solid geometry. Using GeoGebra commands such as Line, Polygon, and Segment, the base and height of the pyramid can be constructed, and the volume can be calculated. Suitable for high school mathematics education or students learning solid geometry.

GeoGebra Commands & Parameters

  1. Line(J, K) → h
  2. Circle(J, base_1) → g
  3. Intersect(g, h, 1) → M
  4. Vector(J, M) → w
  5. Dilate(I, base, H) → L
  6. Vector(H, L) → v
  7. Translate(A, v) → B
  8. Midpoint(A, B) → C
  9. Midpoint(C, A) → D
  10. Translate(D, Vector[w / 2]) → N
  11. AngularBisector(A, N, B) → l
  12. AngularBisector(B, A, N) → k
  13. Intersect(k, l) → O
  14. Dilate(F, height, E) → G
  15. Vector(E, G) → u
  16. Translate(O, u) → D_1
  17. Circle(J, 1) → d
  18. Polygon(A, N, B) → P, b, a, n
  19. Polygon(D_1, A, N) → Q, n_1, n', a_1
  20. Polygon(D_1, B, N) → R, n_2, n'_1, b_1
  21. Polygon(A, D_1, B) → S, b_2, a_2, n'_2
  22. Segment(N, D) → c
  23. Midpoint(N, D) → T
  24. If(VolumeFormula ≟ 1, U) → Z
  25. If(VolumeSolution ≟ 1, V) → A_1
  26. Segment(D_1, O) → m
  27. Midpoint(D_1, O) → C_1
  28. Intersect(b, n) → W
  29. Intersect(a, n) → B_1
  30. Intersect(b, a) → E_1
  31. Polygon(W, B_1, E_1) → t1, e_1, w_1, f