题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075016-25878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075016-15912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075016-57883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075016-88097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075016-40469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075016-15912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075017-92223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075017-41670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075016-25878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075017-40015.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
答案
解析
分析:根据题意,先设EC与AF交与点O,过点O作OG⊥面ABCD,垂足为G;由图分析可得,四棱锥E-ABCD与四棱锥F-ABCD公共部分为四棱锥O-ABCD;根据线面垂直的性质和平面的基本性质,可得CF、OG、AE两两平行且共面;进而在平面FCAE中,计算可得OG的值,依题意,易得底面菱形ABCD的面积,由棱锥体积公式,计算可得答案.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075018-39550.png)
解:根据题意,设EC与AF交与点O,过点O作OG⊥面ABCD,垂足为G;
分析可得,四棱锥E-ABCD与四棱锥F-ABCD公共部分为四棱锥O-ABCD;
依题意,AE,CF都与平面ABCD垂直,OG⊥面ABCD,
可得CF、OG、AE两两平行且共面;
又由AE=2,CF=4,
由平行线的性质,可得OG=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075019-14518.png)
菱形中,对角线AC=4,BD=2
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075019-32049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075019-60685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075019-32049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075019-32049.png)
故其体积为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075019-85204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075019-14518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075019-32049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075017-39781.png)
故选A.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075003-93425.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075003-85249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075003-81546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075004-95865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075004-22465.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075004-80441.gif)
(2)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075005-59081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075005-89792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075005-56551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075005-82498.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075005-89792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022075006-24675.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074952-31007.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074952-64822.gif)
的中点,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074952-79320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074952-69595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074952-16337.gif)
(Ⅰ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074952-36168.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074952-32246.gif)
(Ⅱ)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074953-51431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074953-65167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074953-66938.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074941-59431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074941-42399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074941-40500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074941-30747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074942-68546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074941-42399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074942-96635.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074942-32439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074942-89622.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074942-96242.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074943-34627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074942-32439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074942-89622.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074943-98650.gif)
// 平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074943-15536.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074943-93017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074942-68546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074944-43849.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074937-10188.gif)
(1)求四棱锥P-ABCD的体
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074937-21410.gif)
(2)若E为侧棱PC的中点,求证:PA//平面BDE.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074937-86287.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074937-52751.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074928-66862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074928-17935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074929-77873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074929-15558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074929-96557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074929-18132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074929-77873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022074929-38255.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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