题目
题型:不详难度:来源:
如图,斜三棱柱ABC-A1B1C1的侧面AA1C1C是面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015209-90266.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015209-74963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015209-56670.jpg)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015209-74963.gif)
(2) 求三棱锥A1-ABC的体积.
答案
(1) 略
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015209-84478.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015210-71332.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015210-57103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015210-39545.gif)
知C1到AA1的距离为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015210-41002.gif)
且C1D⊥AA1,所以AA1⊥平面BC1D. 又BC1
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015210-20283.gif)
由(1)知BD⊥AA1,又侧面ABB1A1⊥侧面AA1C1C,所以BD⊥平面AA1C1C,
即B到平面AA1C1C 的距离为BD. 又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015211-92127.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015211-95893.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015211-69505.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015211-43672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015211-17913.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015212-50320.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015212-45948.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015212-26119.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015212-35999.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015212-41917.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015212-35999.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015211-43672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015213-23476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015209-84478.gif)
故三棱锥A1-ABC的体积为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015209-84478.gif)
核心考点
试题【 (本小题满分12分)如图,斜三棱柱ABC-A1B1C1的侧面AA1C1C是面积为的菱形,∠ACC1为锐角,侧面ABB1A1⊥侧面AA1C1C,且A1B=AB=】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
已知长方体ABCD-
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015202-39313.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015202-54151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015202-87742.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015202-65813.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015203-79021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015202-87742.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015203-66086.jpg)
(1)求ED与平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015203-75274.gif)
(2)求二面角E-BD-C的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015154-83107.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015154-60237.gif)
EF∥AC, EF=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015154-79683.gif)
(1)求证:AF∥面BDE
(2)求CF与面DCE所成角的正切值。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015149-45174.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015149-80600.gif)
求证:平面ACD⊥平面PAC;
求异面直线PC与BD所成角的余弦值;
设二面角A—PC—B的大小为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015149-63374.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015149-66031.gif)
四
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-48661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-44349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-73015.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-44524.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-80433.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-61551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-73015.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-83642.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-19092.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-77956.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015140-69283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015140-59457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015140-60822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015140-38377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015140-21974.gif)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015140-56705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015139-73015.gif)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015140-25275.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015140-28607.gif)
已知斜三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015124-33544.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015124-57241.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015124-98154.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015125-75394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015125-57087.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015125-48495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015125-63136.gif)
(1)求证
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015126-39389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015126-21492.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015126-63761.gif)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015126-45834.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015126-58983.gif)
(3)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015127-82919.gif)
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