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Surface Area of a Cuboid: Animated Net Folding

Surface Area of a Cuboid: Animated Net Folding
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2020-08-26 12:59
PolygonVectorSolid GeometryGeometric ConstructionSlider Animation
This example demonstrates a cuboid net folding into a 3‑D cuboid while dynamically showing the total surface area. The key mathematical concepts are solid geometry – cuboid properties, surface‑area computation, and the relationship between a net and its solid. Construction highlights: Vector commands define edge directions; Polygon builds each face; If and Midpoint drive the folding animation logic; Area calculates individual face areas for the sum. Objects such as PA, nHeight, nLength, nWidth, PB_2, PTP, etc., control dimensions and animation parameters. It is suitable for middle‑school geometry lessons on solids, high‑school solid‑geometry review, and interactive self‑study of surface‑area concepts.

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

AI Drawing Prompt Reference

Create a cuboid net composed of six rectangular faces representing the front, back, left, right, top, and bottom sides. Include sliders to control a folding animation that gradually brings the flat net into a three‑dimensional cuboid, while dynamically displaying the total surface area. Each face should be labeled with its length, width, and height dimensions, and the animation should show the area calculation for every face and their sum. Allow the user to adjust the length, width, and height parameters to see how the surface area changes in real time.
The prompt above was compiled from the original drawing commands and is for reference only.