MathPlotAI Logo MathPlotAI

Cuboid Surface Area Calculation

Cuboid Surface Area Calculation
Loading the math board and drawing, please wait…
2020-08-13 14:32
PolygonVectorSolid GeometryGeometric Construction
This GeoGebra example dynamically constructs a cuboid to visually demonstrate surface area calculation and formula application. Core mathematical concepts include rectangular area formulas, solid geometry properties, and surface area problem-solving. Construction highlights involve Vector, Polygon, Midpoint, If, and Area commands to build the cuboid's faces, edges, and vertices, enabling automatic surface area computation. Suitable for middle and high school geometry education, it helps students visualize the origin and steps of surface area calculation in 3D space.

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, PTPF + ((dist * Length[tpf] / 100); Angle[tpf]), PTP + (((dist - 100) * Length[tpa1] / 100); Angle[tpa1])) → TP_3
  15. If(dist < 100, PTPF_1 + ((dist * Length[tpf1] / 100); Angle[tpf1]), PTP_1 + (((dist - 100) * Length[tpsb] / 100); 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

Draw a cuboid with its six faces: front, back, top, bottom, left side, and right side. Use vector and polygon commands to construct these faces and calculate the area of each face. First, create vectors to define the edges of the cuboid, then use these vectors to build polygons, and finally calculate the area of each face.
The prompt above was compiled from the original drawing commands and is for reference only.