IM 6.1.12 课例:什么是表面积?——棱柱表面积动态演示(活动 1 & 2)
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本范例演示棱柱的表面积构成,通过动态展示底面与侧面多边形,帮助学生直观理解表面积由底面面积和侧面面积相加而来。核心数学概念涵盖立体几何、棱柱表面积、多边形面积合并以及面积的加法原理。作图要点:使用 GeoGebra Polygon 命令构建底面与侧面多边形(poly1_2、poly1_3 等),利用 Prism 命令生成棱柱立体,并定义顶点 A_2–H_2、棱边 edgeAE_2、edgeBF_2 等以及各侧面 faceABFE_2、faceBCGF_2、faceCDHG_2、faceADHE_2、faceEFGH_2 对象,实现面与棱的精确标注与动态关联。适合初中(六年级至七年级)几何教学,可用于课堂演示、表面积概念导入或学生自主探究。
GeoGebra 命令及参数
Polygon(A_2, B_2, C_2, D_2) → poly1_2, a_2, b_2, c_2, d_2Prism(poly1_2, E_2) → e_2, F_2, edgeBF_2, edgeCG_2, edgeDH_2, edgeEF_2, edgeFG_2, edgeGH_2, edgeEH_2, G_2, H_2, faceABFE_2, faceBCGF_2, faceCDHG_2, faceADHE_2, faceEFGH_2, edgeAE_2Polygon(A_3, B_3, C_3, D_3) → poly1_3, a_3, b_3, c_3, d_3Prism(poly1_3, E_3) → e_3, F_3, edgeBF_3, edgeCG_3, edgeDH_3, edgeEF_3, edgeFG_3, edgeGH_3, edgeEH_3, G_3, H_3, faceABFE_3, faceBCGF_3, faceCDHG_3, faceADHE_3, faceEFGH_3, edgeAE_3Polygon(A_4, B_4, C_4, D_4) → poly1_4, a_4, b_4, c_4, d_4Prism(poly1_4, E_4) → e_4, F_4, edgeBF_4, edgeCG_4, edgeDH_4, edgeEF_4, edgeFG_4, edgeGH_4, edgeEH_4, G_4, H_4, faceABFE_4, faceBCGF_4, faceCDHG_4, faceADHE_4, faceEFGH_4, edgeAE_4Polygon(A_5, B_5, C_5, D_5) → poly1_5, a_5, b_5, c_5, d_5Prism(poly1_5, E_5) → e_5, F_5, edgeBF_5, edgeCG_5, edgeDH_5, edgeEF_5, edgeFG_5, edgeGH_5, edgeEH_5, G_5, H_5, faceABFE_5, faceBCGF_5, faceCDHG_5, faceADHE_5, faceEFGH_5, edgeAE_5Polygon(A_6, B_6, C_6, D_6) → poly1_6, a_6, b_6, c_6, d_6Prism(poly1_6, E_6) → e_6, F_6, edgeBF_6, edgeCG_6, edgeDH_6, edgeEF_6, edgeFG_6, edgeGH_6, edgeEH_6, G_6, H_6, faceABFE_6, faceBCGF_6, faceCDHG_6, faceADHE_6, faceEFGH_6, edgeAE_6Polygon(A_7, B_7, C_7, D_7) → poly1_7, a_7, b_7, c_7, d_7Prism(poly1_7, E_7) → e_7, F_7, edgeBF_7, edgeCG_7, edgeDH_7, edgeEF_7, edgeFG_7, edgeGH_7, edgeEH_7, G_7, H_7, faceABFE_7, faceBCGF_7, faceCDHG_7, faceADHE_7, faceEFGH_7, edgeAE_7Polygon(A_8, B_8, C_8, D_8) → poly1_8, a_8, b_8, c_8, d_8Prism(poly1_8, E_8) → e_8, F_8, edgeBF_8, edgeCG_8, edgeDH_8, edgeEF_8, edgeFG_8, edgeGH_8, edgeEH_8, G_8, H_8, faceABFE_8, faceBCGF_8, faceCDHG_8, faceADHE_8, faceEFGH_8, edgeAE_8Polygon(A_9, B_9, C_9, D_9) → poly1_9, a_9, b_9, c_9, d_9Prism(poly1_9, E_9) → e_9, F_9, edgeBF_9, edgeCG_9, edgeDH_9, edgeEF_9, edgeFG_9, edgeGH_9, edgeEH_9, G_9, H_9, faceABFE_9, faceBCGF_9, faceCDHG_9, faceADHE_9, faceEFGH_9, edgeAE_9Polygon(A_{10}, B_{10}, C_{10}, D_{10}) → poly1_{10}, a_{10}, b_{10}, c_{10}, d_{10}Prism(poly1_{10}, E_{10}) → e_{10}, F_{10}, edgeBF_{10}, edgeCG_{10}, edgeDH_{10}, edgeEF_{10}, edgeFG_{10}, edgeGH_{10}, edgeEH_{10}, G_{10}, H_{10}, faceABFE_{10}, faceBCGF_{10}, faceCDHG_{10}, faceADHE_{10}, faceEFGH_{10}, edgeAE_{10}Polygon(A_{11}, B_{11}, C_{11}, D_{11}) → poly1_{11}, a_{11}, b_{11}, c_{11}, d_{11}Prism(poly1_{11}, E_{11}) → e_{11}, F_{11}, edgeBF_{11}, edgeCG_{11}, edgeDH_{11}, edgeEF_{11}, edgeFG_{11}, edgeGH_{11}, edgeEH_{11}, G_{11}, H_{11}, faceABFE_{11}, faceBCGF_{11}, faceCDHG_{11}, faceADHE_{11}, faceEFGH_{11}, edgeAE_{11}Polygon(A_1, B_1, C_1, D_1) → poly1_1, a_1, b_1, c_1, d_1Prism(poly1_1, E_1) → e_1, F_1, edgeBF_1, edgeCG_1, edgeDH_1, edgeEF_1, edgeFG_1, edgeGH_1, edgeEH_1, G_1, H_1, faceABFE_1, faceBCGF_1, faceCDHG_1, faceADHE_1, faceEFGH_1, edgeAE_1Polygon(A_{12}, B_{12}, C_{12}, D_{12}) → poly1_{12}, a_{12}, b_{12}, c_{12}, d_{12}Prism(poly1_{12}, E_{12}) → e_{12}, F_{12}, edgeBF_{12}, edgeCG_{12}, edgeDH_{12}, edgeEF_{12}, edgeFG_{12}, edgeGH_{12}, edgeEH_{12}, G_{12}, H_{12}, faceABFE_{12}, faceBCGF_{12}, faceCDHG_{12}, faceADHE_{12}, faceEFGH_{12}, edgeAE_{12}Polygon(E, B, C, D) → poly1, a, b, c, d
AI 绘图提示语参考
绘制一个棱柱的表面展开图,包括底面多边形、侧面矩形面和棱线。首先绘制一个四边形底面,然后以该底面为底构造一个棱柱,显示棱柱的侧面展开图,包括底面多边形、侧面矩形面和棱线。
以上提示语为根据原始绘图命令整理而来,仅供参考。