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Prism Project

Prism Project
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2016-05-11 21:49
VectorTrigonometrySolid GeometryOptimizationGeometric Construction
This example demonstrates the geometric construction and related calculations of prisms. It involves core mathematical concepts including area, volume, surface area, rational numbers, sequences and series, optimization problems, logic, and isosceles triangles. The construction utilizes commands and objects such as Polygon, OrthogonalLine, Point, Segment, Vector, Translate, Mirror, Dilate, Intersect, Distance, and LaTeX. It is suitable for high school students studying solid geometry, coordinate geometry, and optimization problems.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, f, F, g, h, i, j, k, C, D, E
  2. OrthogonalLine(A, f) → l
  3. Point(l) → G
  4. Segment(A, G) → m
  5. Vector(A, G) → u
  6. Translate(poly1, u) → poly1'
  7. OrthogonalLine(G, u, xOyPlane) → n
  8. Mirror(poly1', n) → poly1''
  9. Dilate(A, 6, A) → A'
  10. Dilate(B, 6, A) → B'
  11. Segment(A', B') → f'
  12. OrthogonalLine(B', f') → p
  13. Intersect(n, p) → H
  14. Polygon(A, B', H, G) → poly2, a, b', h_1, g_1
  15. Distance(A, B) → distanceAB
  16. Distance(A, G) → distanceAG
  17. Vector(A, B) → v
  18. Translate(I, v) → I'
  19. LaTeX(VolumePrism, true, true) → text1
  20. Vector(A, G) → w
  21. Translate(J, w) → J'
  22. LaTeX(SurfaceAreaPrism, true, true) → text2