名校
1 . 如图,在直四棱柱
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b05db872c7a37e0d06ca9f0278f9562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f8caf1d83ac27191a7a4ce3d81c769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5fb45af7400c71ac728f9dfa09a5cb.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d30832deeebfc30b1799624e75b75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223036d27be5914db50fbd5cb19d4212.png)
:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/727ef02f-bf3c-4f85-8b52-52dc0d6654f1.png?resizew=182)
(1)求证:
平面
;
(2)现将与四棱柱
形状和大小完全相同的两个四棱柱拼成一个新的四棱柱,规定:若拼成的新四棱柱形状和大小完全相同,则视为同一种拼接方案,问共有几种不同的拼接方案?在这些拼接成的新四棱柱中,记其中最小的表面积为
,写出
的解析式;(直接写出答案,不必说明理由)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b05db872c7a37e0d06ca9f0278f9562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f8caf1d83ac27191a7a4ce3d81c769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5fb45af7400c71ac728f9dfa09a5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5cab760038d20eac10fe6108fbb334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d30832deeebfc30b1799624e75b75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223036d27be5914db50fbd5cb19d4212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b377f632949bff36083a5464113387fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/727ef02f-bf3c-4f85-8b52-52dc0d6654f1.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)现将与四棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e6cb8d4e39fa44f71df04b74f123f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e6cb8d4e39fa44f71df04b74f123f4.png)
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