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Net of Pyramid by txywishes

Net of Pyramid by txywishes
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2019-07-16 08:46
VectorSolid GeometryGeometric Construction
In collections Nets of Solid Figures (Primary 6)
This example demonstrates the net of a pyramid. Key mathematical concepts include the structure of a pyramid in solid geometry. Using GeoGebra commands such as Sequence, Polygon, Line, etc., the net of a pyramid can be constructed. Suitable for students at junior high school level and above.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[A, ((360 * ° / n) * k), O], k, 0, n - 1, 1) → Vertices
  2. Polygon(Vertices) → Polygon
  3. Line(O, zAxis) → a
  4. Point(a) → V
  5. Segment(O, V) → Height
  6. Segment(A, V) → SlantEdge
  7. Vector((0, 0, 1)) → Z
  8. LineBisector(Element[Vertices, 1], Element[Vertices, 2]) → ReferencePerpendicularBisector
  9. Intersect(ReferencePerpendicularBisector, Line[Element[Vertices, 1], Element[Vertices, 2]]) → ReferenceIntersectionPoint
  10. Vector(O, ReferenceIntersectionPoint) → ReferenceVector
  11. UnitVector(ReferenceVector) → ReferenceUnitVector
  12. Sequence(Vector[Rotate[ReferenceUnitVector, ((360 * ° / n) * k), O]], k, 0, n - 1, 1) → ReferenceAllUnitVector
  13. Circle(Element[Vertices, 1], SlantEdge) → c
  14. Circle(Element[Vertices, 2], SlantEdge) → d
  15. Intersect(c, d) → B, C, ,
  16. Segment(O, C) → FlattenLength
  17. Sequence(O + ((FlattenLength * cos(angle)) * Element[ReferenceAllUnitVector, k]) + ((Height * sin(angle)) * Z), k, 1, n, 1) → AllVertices
  18. Polygon(Element[Vertices, 1], Element[AllVertices, 1], Element[Vertices, 2]) → poly1, b, e, f
  19. Polygon(Element[Vertices, 2], Element[AllVertices, 2], Element[Vertices, 3]) → poly2, g, h, i
  20. Sequence(Polygon[Element[Vertices, k], Element[AllVertices, k], Element[Vertices, k + 1]], k, 1, n - 1, 1) → AllTriangles
  21. Polygon(Element[Vertices, n], Element[AllVertices, n], Element[Vertices, 1]) → FinalTriangle, j, k, l