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金字塔的表面积

金字塔的表面积
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2019-06-27 00:09
多边形立体几何几何作图
①本范例演示了如何使用 GeoGebra 构建金字塔并计算其表面积；②涉及的核心数学概念包括立体几何、多边形面积计算、三角形性质；③作图要点——从下方『构造摘要』提炼用到了 Pyramid, Prism 命令，以及 A, B, C, D, E, F, G, H, I 等对象，还涉及 faceABDC, faceACE_1, edgeAC_1 等多边形和边对象的定义；④适合高中阶段学习立体几何的学生，可用于理解金字塔结构及表面积计算方法。

GeoGebra 命令及参数

  1. Pyramid(A, C, D, B, E) → a, faceABDC, edgeAE_1, edgeCE_1, edgeDE_1, edgeBE_1, faceACE_1, faceCDE_1, faceBDE_1, faceABE_1, edgeAC_1, edgeCD_1, edgeBD_1, edgeAB_1
  2. Pyramid(I, F, B, D, E) → c, faceBDIF, edgeEI_1, edgeEF_1, edgeBE_2, edgeDE_2, faceEFI, faceBEF_1, faceBDE, faceDEI_1, edgeFI, edgeBF_1, edgeBD, edgeDI_1
  3. Pyramid(F, G, A, B, E) → d, faceABFG, edgeEF, edgeEG_1, edgeAE_2, edgeBE, faceEFG, faceAEG_1, faceABE, faceBEF, edgeFG, edgeAG_1, l, edgeBF
  4. Pyramid(G, H, C, A, E) → e, faceACHG, edgeEG, edgeEH_1, edgeCE_2, edgeAE, faceEGH, faceCEH_1, faceACE, faceAEG, edgeGH, edgeCH_1, w, edgeAG
  5. Pyramid(H, I, D, C, E) → f, faceCDIH, edgeEH, edgeEI, edgeDE, edgeCE, faceEHI, faceDEI, faceCDE, faceCEH, edgeHI, edgeDI, edgeCD, h
  6. Prism(O, K, J, N, P) → b, R, edgeKO, edgeJK, edgeJN, edgeNO, edgeOP, edgeKR, edgeJS, edgeNT, edgePR, edgeRS, S, edgeST, edgePT, T, faceJKON, faceKOPR, faceJKRS, faceJNTS, faceNOPT, facePRST