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Cuboid Surface Area Demonstration

Cuboid Surface Area Demonstration
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2015-11-28 03:41
Solid GeometryGeometric Construction
This example demonstrates the folding of a cuboid from a flat plane into a 3D shape. Key mathematical concepts include the calculation of a cuboid's surface area. Using GeoGebra commands such as Vector, Polygon, and Area, the dimensions of the cuboid can be adjusted and its surface area calculated. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Vector(PTP_1, PB_3) → tpsb
  2. Vector(PTPF_1, PTP_1) → tpf1
  3. Vector(PTP, PB_2) → tpa1
  4. Vector(PTPF, PTP) → tpf
  5. Vector(PBK, PB) → bk1
  6. Vector(PBK_1, PB_1) → bk11
  7. Vector(PFT_1, PB_3) → ftb13
  8. Vector(PFT, PB_2) → fta1
  9. Vector(PSB_1, PB_3) → sbb13
  10. Vector(PSB, PB_1) → sbb
  11. Vector(PSF_1, PB_2) → sfa1
  12. Vector(PSF, PB) → sfb
  13. Polygon(SF_3, SF, SF_1, SF_2) → aSideFront, a, b, c, d
  14. If(dist < 100.0, PTPF + (dist * Length[tpf] / 100.0; Angle[tpf]), PTP + ((dist - 100.0) * Length[tpa1] / 100.0; Angle[tpa1])) → TP_3
  15. If(dist < 100.0, PTPF_1 + (dist * Length[tpf1] / 100.0; Angle[tpf1]), PTP_1 + ((dist - 100.0) * Length[tpsb] / 100.0; Angle[tpsb])) → TP_2
  16. Polygon(TP_3, TP_2, TP_1, TP) → aTop, a_1, b_1, c_1, d_1
  17. Polygon(BK_3, BK_2, BK_1, BK) → aBack, a_2, b_2, c_2, d_2
  18. Polygon(BT, BT_1, BT_2, BT_3) → aBottom, a_3, b_3, c_3, d_3
  19. Polygon(SB, SB_1, SB_2, SB_3) → aSideBack, a_4, b_4, c_4, d_4
  20. Polygon(FT, FT_1, FT_2, FT_3) → aFront, a_5, b_5, c_5, d_5
  21. Polygon(NA_2, NA, NA_1, NA_3) → planBottom, na_2, na, na_1, na_3
  22. Polygon(NA_2, NA_3, NFT_1, NFT) → planFront, na_4, na_5, nft_1, nft
  23. Polygon(NA, NSF, NSF_1, NA_2) → planSideFront, na_6, nsf, nsf_1, na_7
  24. Polygon(NA_1, NSB, NSB_1, NA_3) → planSideBack, na_8, nsb, nsb_1, na_9
  25. Polygon(NA, NBK, NBK_1, NA_1) → planBack, na_{10}, nbk, nbk_1, na_{11}
  26. Polygon(NBK, NTPT, NTPF_1, NBK_1) → planTop, nbk_2, ntpt, ntpf_1, nbk_3
  27. Midpoint(nft_1) → Hnf
  28. Midpoint(ntpf_1) → Hpl
  29. Midpoint(nbk_1) → Hpb
  30. Midpoint(b_1) → HXts
  31. Midpoint(d_2) → HXbs
  32. Midpoint(c_5) → HXfs
  33. Area(BK_3, BK_2, BK_1, BK) → bb