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Volume of a Triangular Prism Demo

Volume of a Triangular Prism Demo
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2012-12-19 22:23
Solid GeometryCalculusGeometric Construction
This example demonstrates how to draw and calculate the volume of a triangular prism using GeoGebra. It involves core mathematical concepts such as volume calculation formulas, geometric construction, and spatial geometry. Key GeoGebra commands/objects used include Point, Segment, Polygon, and Translate, as summarized below. Suitable for high school students learning solid geometry and volume calculations, or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Point(Circle[A, tinggi]) → B
  2. Segment(A, B) → a
  3. Point(Circle[A, lebar]) → C
  4. Segment(A, C) → b
  5. Point(Circle[A, panjang]) → D
  6. Segment(A, D) → c
  7. Point(Circle[A_1, lebar]) → C_1
  8. Segment(A_1, C_1) → b_1
  9. Point(Circle[A_2, lebar]) → C_2
  10. Segment(A_2, C_2) → b_2
  11. Point(Circle[A_4, tinggi]) → B_1
  12. Segment(A_4, B_1) → a_1
  13. Point(Circle[A_6, tinggi]) → B_2
  14. Segment(A_6, B_2) → a_2
  15. Point(Circle[A_{10}, panjang]) → D_1
  16. Segment(A_{10}, D_1) → c_1
  17. Point(Circle[A_{13}, panjang]) → D_2
  18. Segment(A_{13}, D_2) → c_2
  19. Point(Circle[A_{16}, panjang]) → D_3
  20. Segment(A_{16}, D_3) → c_3
  21. Segment(D, D_2) → d
  22. Segment(D_2, D_3) → e
  23. Polygon(B_1, D_2, D, C) → poly1, b_3, d_2, d_1, c_4
  24. Polygon(B_1, B, A, C) → poly2, b_4, b_5, a_3, c_5
  25. Polygon(B_1, C, D_1, D_3) → poly3, b_6, c_6, d_3, d_4
  26. Polygon(D_2, D_3, D_1, D) → poly4, d_5, d_6, d_7, d_8
  27. Polygon(B, D_2, D, A) → poly5, b_7, d_9, d_{10}, a_4
  28. Polygon(B_1, D_3, D_2, B) → poly11, b_{10}, d_{14}, d_{15}, b_{11}
  29. Polygon(A, C, D_1, D) → poly12, a_5, c_{14}, d_{16}, d_{17}
  30. Point(Circle[A_{27}, panjang]) → D_5
  31. Segment(A_{27}, D_5) → c_{15}
  32. Point(Circle[A_{31}, lebar]) → C_6
  33. Segment(A_{31}, C_6) → b_{13}
  34. Point(Circle[A_{36}, panjang]) → D_7
  35. Segment(A_{36}, D_7) → c_{17}
  36. Point(Circle[A_{37}, lebar]) → C_7
  37. Segment(A_{37}, C_7) → b_{14}
  38. Point(Circle[A_{41}, tinggi]) → B_4
  39. Segment(A_{41}, B_4) → a_7
  40. Point(Circle[A_{42}, lebar]) → C_8
  41. Segment(A_{42}, C_8) → b_{15}
  42. Point(Circle[A_{46}, tinggi]) → B_5
  43. Segment(A_{46}, B_5) → a_8
  44. Point(Circle[A_{47}, lebar]) → C_9
  45. Segment(A_{47}, C_9) → b_{16}
  46. Translate(B_1, Vector[geser1 * Vector[B_1, B_2]]) → pryB_1
  47. Translate(B, Vector[geser1 * Vector[B_1, B_2]]) → pryB
  48. Translate(A, Vector[geser1 * Vector[B_1, B_2]]) → pryA
  49. Translate(C, Vector[geser1 * Vector[B_1, B_2]]) → pryC
  50. Translate(D, Vector[geser1 * Vector[B_1, B_2]]) → pryD
  51. Translate(D_2, Vector[geser1 * Vector[B_1, B_2]]) → pryD_2
  52. Translate(B_1, Vector[geser2 * Vector[B_1, B_2]]) → pryBB
  53. Translate(B_2, Vector[geser2 * Vector[B_1, B_2]]) → pryB_2
  54. Translate(C, Vector[geser2 * Vector[B_1, B_2]]) → pryCC
  55. Translate(C_2, Vector[geser2 * Vector[B_1, B_2]]) → pryC_2
  56. Translate(D, Vector[geser2 * Vector[B_1, B_2]]) → pryDD
  57. Polygon(pryB_1, pryD_2, pryD, pryC) → poly6, pryb_1, pryd_2, pryd, pryc
  58. Translate(D_2, Vector[geser2 * Vector[B_1, B_2]]) → pryDD_2
  59. Polygon(pryBB, pryDD_2, pryDD, pryCC) → poly7, prybb, prydd_2, prydd, prycc
  60. Polygon(pryB_1, pryB, pryA, pryC) → poly8, pryb_2, pryb, prya, pryc_1
  61. Polygon(pryB_1, pryD_2, pryB) → poly9, pryb_3, pryb_4, pryd_1
  62. Polygon(pryA, pryC, pryD) → poly10, pryd_3, prya_1, pryc_2
  63. Polygon(pryB, pryA, pryD, pryD_2) → poly13, pryb_5, prya_2, pryd_4, pryd_5
  64. Polygon(pryBB, pryCC, pryC_2, pryB_2) → poly14, prybb_1, prycc_1, pryc_3, pryb_6
  65. Polygon(pryB_2, pryC_2, pryDD, pryDD_2) → poly15, pryb_7, pryc_4, prydd_1, prydd_3
  66. Polygon(pryBB, pryB_2, pryDD_2) → poly16, prydd_4, prybb_2, pryb_8
  67. Polygon(pryCC, pryC_2, pryDD) → poly17, prydd_5, prycc_2, pryc_5
  68. Polygon(pryA, pryD, pryC) → poly18, pryc_6, prya_3, pryd_6

AI Drawing Prompt Reference

Draw a triangular prism by first creating a triangular base at point A, then constructing other points and segments through point A and the base edges to form two parallel triangular bases. Next, construct vertical segments through point A and base edges to connect the two triangular bases, forming the prism's side faces. Finally, translate the base triangle to obtain the other base of the prism.
The prompt above was compiled from the original drawing commands and is for reference only.