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Construct Rectangular Prisms with Given Surface Area

Construct Rectangular Prisms with Given Surface Area
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2020-03-23 02:20
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to construct rectangular prisms given a specific surface area. Key mathematical concepts include the calculation of the surface area of a rectangular prism. Using GeoGebra commands such as Ray, Prism, Net, etc., the dimensions of the prism can be dynamically adjusted. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Ray((0, 0, 0), (1, 0, 0)) → f
  2. Ray((0, 0, 0), (0, 1, 0)) → g
  3. Ray((0, 0, 0), (0, 0, 1)) → h
  4. Prism(E, A, D, B, C) → d, F, edgeAE, edgeAD, edgeBD, edgeBE, edgeCE, edgeAF, edgeDG, edgeBH, edgeCF, edgeFG, G, edgeGH, edgeCH, H, faceADBE, faceAECF, faceADGF, faceBDGH, faceBECH, faceCFGH
  5. Net(d, openclose) → i, I, R, S, T, U, V, faceIJKL, faceIJNM, faceJKPO, faceKLRQ, faceILST, J, faceMNUV, edgeIJ, edgeJK, edgeKL, edgeIL, edgeIM, edgeMN, edgeJN, edgeJO, edgeOP, K, edgeKP, edgeKQ, edgeQR, edgeLR, edgeLS, edgeST, edgeIT, edgeNU, edgeUV, edgeMV, L, M, N, O, P, Q
  6. Sequence(Segment[(i, 0, 0), (i, WIDTH, 0)], i, 1, LENGTH - 1, 1) → L_1
  7. Translate(L_1, Vector[A, F]) → L_2
  8. Sequence(Segment[(0, i + 1, 0), (LENGTH, i + 1, 0)], i, 0, WIDTH - 2) → L_3
  9. Translate(L_3, Vector[A, F]) → L_4
  10. Vector(M, V) → u
  11. Sequence((x(M) + i, y(M), z(M)), i, 1, LENGTH - 1, 1) → L_5
  12. Translate(L_5, u) → L_6
  13. Sequence(Segment[Element[L_5, i], Element[L_6, i]], i, 1, LENGTH - 1) → L_7
  14. Sequence((x(M), y(M) + (i * y(u) / WIDTH), z(M) + (i * z(u) / WIDTH)), i, 1, WIDTH - 1, 1) → L_8
  15. Vector(V, U) → v
  16. Translate(L_8, v) → L_9
  17. Sequence(Segment[Element[L_8, i], Element[L_9, i]], i, 1, WIDTH - 1) → L_{10}
  18. Vector(A, O) → w
  19. Sequence((x(A) + (i * x(w) / HEIGHT), y(A), z(A) + (i * z(w) / HEIGHT)), i, 1, HEIGHT - 1, 1) → L_{11}
  20. Vector(O, P) → l
  21. Translate(L_{11}, l) → L_{12}
  22. Sequence(Segment[Element[L_{11}, i], Element[L_{12}, i]], i, 1, HEIGHT - 1) → L_{13}
  23. Sequence((x(O), y(O) + (i * y(l) / WIDTH), z(O) + (i * z(l) / WIDTH)), i, 1, WIDTH - 1, 1) → L_{14}
  24. Translate(L_{14}, Vector[(-w)]) → L_{15}
  25. Sequence(Segment[Element[L_{14}, i], Element[L_{15}, i]], i, 1, WIDTH - 1) → L_{16}
  26. Mirror(L_{13}, k) → L_{17}
  27. Mirror(L_{16}, k) → L_{18}
  28. Vector(D, Q) → m
  29. Sequence((x(B) + (i * x(v) / LENGTH), y(B), z(B)), i, 1, LENGTH - 1, 1) → L_{19}
  30. Translate(L_{19}, m) → L_{20}
  31. Sequence(Segment[Element[L_{19}, i], Element[L_{20}, i]], i, 1, LENGTH - 1) → L_{21}
  32. Sequence((x(B), y(B) + (i * y(m) / HEIGHT), z(B) + (i * z(M) / HEIGHT)), i, 1, HEIGHT - 1, 1) → L_{22}
  33. Translate(L_{22}, v) → L_{23}
  34. Sequence(Segment[Element[L_{22}, i], Element[L_{23}, i]], i, 1, HEIGHT - 1) → L_{24}
  35. Mirror(L_{21}, n) → L_{25}
  36. Mirror(L_{24}, n) → L_{26}
  37. RandomElement(l2) → a
  38. Mode(l2) → l3
  39. IndexOf(a, l2) → e
  40. Element(l2, e + 1) → j
  41. Element(l2, e + 2) → o
  42. Element(l2, e + 3) → p
  43. CountIf(x ≟ a, l2) → q
  44. If(q ≟ 1, "There is 1 solution here.", q ≟ 2, "There are 2 solutions here.", q ≟ 3, "There are 3 solutions here.") → text2

AI Drawing Prompt Reference

Draw a rectangular prism with a given surface area. Start by creating rays for the three axes, then construct the prism based on the given dimensions. Next, draw the net of the prism. Finally, generate the faces and edges of the prism based on the net.
The prompt above was compiled from the original drawing commands and is for reference only.