解题方法
1 . 将一个边长为
的正六边形
(图
)沿
对折,形成如图
所示的五面体,其中,底面
是正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/0f02daa5-242a-428e-9be1-dd001ef68e52.png?resizew=464)
(1)求五面体(图
)中
的余弦值:
(2)如图
,点
分别为棱
上的动点.
①求
周长的最大值,并说明理由;
②当
周长最大时,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/0f02daa5-242a-428e-9be1-dd001ef68e52.png?resizew=464)
(1)求五面体(图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3f19ab76b27b47aeaaf4a66f0e580b.png)
(2)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb025beb66dc609261deac78327954c.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f3f9f4edf520ce61c8e83a2be394d6.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f3f9f4edf520ce61c8e83a2be394d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546990b47ca3fdd5681de4749246d38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
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