解题方法
1 . 如图①,矩形ABCD中,AB=4,AD=2,E,F分别为AB,DC的中点.将四边形AEFD沿EF折起至四边形
的位置,如图②.
![](https://img.xkw.com/dksih/QBM/2021/7/5/2757823182479360/2779884305514496/STEM/9ebc79d532c3457a8a7917e91b17fbdb.png?resizew=490)
(1)求证:EF⊥平面
;
(2)若点
在平面EFCB上的射影为BE的中点,求三棱锥
的体积;
(3)当平面
与平面EFCB垂直时,作正方体
如图③.若平面
∥平面
,且平面
截该正方体所得图形的面积为S.
①若C∈
,则S= ;
②S的最大值为 .(直接写出结果)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ccd49a0c3ccd22943c15ed7bf0f4c2.png)
![](https://img.xkw.com/dksih/QBM/2021/7/5/2757823182479360/2779884305514496/STEM/9ebc79d532c3457a8a7917e91b17fbdb.png?resizew=490)
(1)求证:EF⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641d9688e81760c02d0dfc4ba015afb1.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945fbe95bfb4e8e37e619e2d767efef6.png)
(3)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ccd49a0c3ccd22943c15ed7bf0f4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bc49d40da6aebbb370be30fa2e6c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecba239ca1f109309bf14fab784ea827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①若C∈
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
②S的最大值为 .(直接写出结果)
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