已知菱形
的边长为
,
,如图1.沿对角线
将
向上折起至
,连接
,构成一个四面体
,如图2.
;
(2)若
,求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c967c9b3f669ea78edd838e1d8b59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417104247ce266ae42c3a9860f387272.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685534ba47e83433200ce29660875118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
更新时间:2021-11-13 21:22:38
|
相似题推荐
【推荐1】在四棱锥Q-ABCD中,底面ABCD是正方形,若
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/e87c7abe-6fde-4b36-8a0b-b7bfebd50666.png?resizew=180)
(1)证明:平面
⊥平面
;
(2)求四棱锥
的体积与表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3d0f667ef7ca851f514f2e742a8624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a512bcb83a2e952d2f1f877f1ceaa5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/e87c7abe-6fde-4b36-8a0b-b7bfebd50666.png?resizew=180)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40cae1138ce408cf7ebbe14f152d6e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
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【推荐2】如图,四棱锥
的底面
是边长为2的菱形,
.已知
.
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285433262080/1571285438873600/STEM/01ac40461d5d4853ba9100835a2dbcc6.png?resizew=302)
(Ⅰ)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
(Ⅱ)若
为
的中点,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4c7ccee57161162e10294aecf2b0b4.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285433262080/1571285438873600/STEM/01ac40461d5d4853ba9100835a2dbcc6.png?resizew=302)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95e78927443bbadb5bf60f1c836ea24.png)
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解题方法
【推荐1】空间中到一个三角形的三个顶点距离相等的点组成的集合是什么图形?
您最近一年使用:0次
解答题-问答题
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【推荐2】如图,已知四棱锥
的底面为矩形,
为
的中点,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/28/e089f593-0914-4f50-be83-3c61d2a76ee6.png?resizew=194)
(1)证明:
平面
;
(2)若
,
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee27ae6e34c2464ca5b6281c3a262caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/28/e089f593-0914-4f50-be83-3c61d2a76ee6.png?resizew=194)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc7e774e4ae40c23bf4ceed179230ca.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c90ff9402bacab8319385d3bab70dcc.png)
(i)求的长;
(ii)求与平面
所成角的正弦值.
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