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Volume of a pyramid ABCD in 3D space

Volume of a pyramid ABCD in 3D space
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2015-11-28 22:26
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to construct and calculate the volume of a pyramid ABCD in 3D space. Key math concepts include volume formulas, polygon construction, vector operations, and analytical geometry. It uses commands like Vector, Plane, Polygon, Segment, Pyramid, LaTeX, and Line in GeoGebra for construction. Suitable for high school solid geometry teaching and geometric construction practice.

GeoGebra Commands & Parameters

  1. Vector(B, A) → BA
  2. Vector(B, C) → BC
  3. Plane(A, B, C) → a
  4. Polygon(A, B, C) → poly1, c, a_1, b
  5. Vector(B, E) → n
  6. Segment(A, D) → d
  7. Pyramid(A, B, C, D) → e, faceABC, edgeCD, faceABD, faceBCD, faceACD, edgeAB, edgeBC, edgeAC, edgeAD, edgeBD
  8. LaTeX(A, true, true) → text1
  9. LaTeX(B, true, true) → text2
  10. LaTeX(C, true, true) → text3
  11. Line(A, n) → j

AI Drawing Prompt Reference

Draw a pyramid in 3D space with a triangular base and an apex directly above the centroid of the base. Start by constructing the triangular base with its three vertices and edges. Then, draw a line segment from one vertex of the base to the apex. Next, calculate and display the normal vector of the plane containing the base, and draw a line segment from one vertex of the base along this vector. Finally, label the coordinates of the three vertices and show the faces and edges of the pyramid.
The prompt above was compiled from the original drawing commands and is for reference only.