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Volume of a Rectangular Prism by Stacey Goode

Volume of a Rectangular Prism by Stacey Goode
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2017-05-17 13:09
Solid GeometryCalculusGeometric Construction
This example demonstrates the calculation of a rectangular prism's volume using GeoGebra, showcasing 3D geometry, algebra, and derivatives. It constructs the prism and its volume formula dynamically, involving commands like Vector, Line, Intersect, Segment, Polygon, and Midpoint. Ideal for high school geometry and calculus introduction.

GeoGebra Commands & Parameters

  1. Vector(((0.75 * width), (0.5 * width))) → w
  2. Vector((0, height)) → z
  3. Vector((((-0.75) * length), (0.4 * length))) → u
  4. Line(C, z) → d
  5. Line(B, w) → e
  6. Line(B, u) → f
  7. Line(A, z) → g
  8. Intersect(f, g) → D
  9. Intersect(d, e) → E
  10. Segment(A, D) → h
  11. Segment(D, B) → i
  12. Segment(B, E) → j
  13. Segment(E, C) → k
  14. Line(D, j) → l
  15. Line(E, i) → m
  16. Intersect(l, m) → F
  17. Segment(D, F) → n
  18. Segment(F, E) → p
  19. Polygon(D, A, O, B) → poly1, d_1, a_1, o, b_1
  20. Polygon(D, F, E, B) → poly2, d_2, f_1, e_1, b_2
  21. Polygon(O, C, E, B) → poly3, o_1, c_1, e_2, b_3
  22. Midpoint(o_1) → G
  23. Midpoint(c_1) → H
  24. Midpoint(a_1) → I