MathPlotAI Logo MathPlotAI

Surface Area of Rectangular Prism

Surface Area of Rectangular Prism
Loading the math board and drawing, please wait…
2020-03-30 12:54
VectorSolid GeometryGeometric Construction
This example demonstrates how to calculate the surface area of a rectangular prism. It involves core mathematical concepts such as area calculation of geometric figures and the relationship between points, lines, and planes in three-dimensional space. Key GeoGebra commands and objects used in the construction include Ray, Prism, Net, Sequence, Translate, Vector, and Mirror. Suitable for middle school students and above learning solid geometry or for mathematical teaching demonstrations.

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}