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统编高中数学第二册《空间图形》部分,导出了棱台中截面(与两底等距离的截面)面积公式:S_0=(S′~(1/2)+S~(1/2)/2)~2(S_0表示中截面面积,S′、S分别表示上、下两底面面积)。注意到:S_0只与棱台上、下底面积及截面与上、下两底面距离之比有关,而不依赖于台体的高度。对这个问题有兴趣的读者自然会提出这样的问题: (1)截面与上、下两底面的距离比为λ(不一定是中截面)时,其面积“S_0”的表达式怎样? (2)截面分棱台上、下两部分的侧面积
In the second volume of the “Space Graphics” section of the Mathematics Book 2 of the Senior High School, the section formula of the cross section of the truncated pyramid (a section equidistant from the two bases) is derived: S_0=(S′~(1/2)+S~(1/2)/ 2) ~2 (S_0 means medium cross-sectional area, S’, S mean upper and lower bottom surface area). Note that S_0 only relates to the ratio of the area and cross section of the upper and lower bases of the prism table to the distance between the upper and lower base, and does not depend on the height of the table body. Readers interested in this issue will naturally ask such questions: (1) What is the expression of the area “S_0” when the ratio of the distance between the cross-section and the upper and lower surfaces is λ (not necessarily the middle section)? (2 ) Side area of the upper and lower sections of the splitting table