长方体表面积演示 by SHAMSUDIN BIN MOHD ROSLI
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该范例演示了一个长方体从平面折叠成立体的过程。核心数学概念包括长方体的表面积计算。使用了Vector, Polygon, If, Midpoint, Area等GeoGebra命令。适合初中及以上学生学习立体几何。
GeoGebra 命令及参数
Vector(PTP_1, PB_3) → tpsbVector(PTPF_1, PTP_1) → tpf1Vector(PTP, PB_2) → tpa1Vector(PTPF, PTP) → tpfVector(PBK, PB) → bk1Vector(PBK_1, PB_1) → bk11Vector(PFT_1, PB_3) → ftb13Vector(PFT, PB_2) → fta1Vector(PSB_1, PB_3) → sbb13Vector(PSB, PB_1) → sbbVector(PSF_1, PB_2) → sfa1Vector(PSF, PB) → sfbPolygon(SF_3, SF, SF_1, SF_2) → aSideFront, a, b, c, dIf(dist < 100.0, PTPF + (dist * Length[tpf] / 100.0; Angle[tpf]), PTP + ((dist - 100.0) * Length[tpa1] / 100.0; Angle[tpa1])) → TP_3If(dist < 100.0, PTPF_1 + (dist * Length[tpf1] / 100.0; Angle[tpf1]), PTP_1 + ((dist - 100.0) * Length[tpsb] / 100.0; Angle[tpsb])) → TP_2Polygon(TP_3, TP_2, TP_1, TP) → aTop, a_1, b_1, c_1, d_1Polygon(BK_3, BK_2, BK_1, BK) → aBack, a_2, b_2, c_2, d_2Polygon(BT, BT_1, BT_2, BT_3) → aBottom, a_3, b_3, c_3, d_3Polygon(SB, SB_1, SB_2, SB_3) → aSideBack, a_4, b_4, c_4, d_4Polygon(FT, FT_1, FT_2, FT_3) → aFront, a_5, b_5, c_5, d_5Polygon(NA_2, NA, NA_1, NA_3) → planBottom, na_2, na, na_1, na_3Polygon(NA_2, NA_3, NFT_1, NFT) → planFront, na_4, na_5, nft_1, nftPolygon(NA, NSF, NSF_1, NA_2) → planSideFront, na_6, nsf, nsf_1, na_7Polygon(NA_1, NSB, NSB_1, NA_3) → planSideBack, na_8, nsb, nsb_1, na_9Polygon(NA, NBK, NBK_1, NA_1) → planBack, na_{10}, nbk, nbk_1, na_{11}Polygon(NBK, NTPT, NTPF_1, NBK_1) → planTop, nbk_2, ntpt, ntpf_1, nbk_3Midpoint(nft_1) → HnfMidpoint(ntpf_1) → HplMidpoint(nbk_1) → HpbMidpoint(b_1) → HXtsMidpoint(d_2) → HXbsMidpoint(c_5) → HXfsArea(BK_3, BK_2, BK_1, BK) → bb
AI 绘图提示语参考
画一个长方体,先展示其展开图,然后通过折叠形成三维立体形状。关键部分包括长方体的六个面,用明暗关系区分,并标注每个面的面积。从展开图开始,依次绘制顶面、前面、侧面、后面和底面,最后将它们折叠成完整的长方体,展示其三维结构。
以上提示语为根据原始绘图命令整理而来,仅供参考。