如图
所示,将一张长为
,宽为
的长方形纸片沿虚线剪成
个直角三角形,拼成如图
的正方形
(相邻纸片之间不重叠,无缝隙),若正方形
的面积为
,中间空白处的正方形
的面积为
,则:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
______ ;
(2)原长方形纸片的周长是______ (用m表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff8245c281711ddde3aedd6a5eb76f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
(2)原长方形纸片的周长是
![](https://img.xkw.com/dksih/QBM/2022/7/14/3022020837294080/3033730293399552/STEM/b454086ec56e412a83e5129215049212.png?resizew=350)
更新时间:2022-07-30 14:42:59
|
【知识点】 完全平方公式在几何图形中的应用解读
相似题推荐
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【推荐1】如图1,将长方形纸片沿图中虚线剪成四个形状和大小相同的小长方形,然后拼成如图2的一个大正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/56e1a385-96ea-44fc-bbde-ab86d560e7ad.png?resizew=349)
(1)若图1中大长方形的长为4,宽为2,则图2中小正方形(阴影部分)的面积![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
________ ;
(2)若图1中大长方形的长为
,宽为
,则图2中小正方形(阴影部分)的面积![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
_______ (用含m、n的式子表示).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/56e1a385-96ea-44fc-bbde-ab86d560e7ad.png?resizew=349)
(1)若图1中大长方形的长为4,宽为2,则图2中小正方形(阴影部分)的面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
(2)若图1中大长方形的长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
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【推荐2】如图,大正方形是由两个小正方形和两个长方形拼成的,通过用两种方法计算图中阴影正方形的面积,可以得到的乘法公式是_______ .
![](https://img.xkw.com/dksih/QBM/2020/6/11/2482378567786496/2484640764297216/STEM/8d415544b75a45faa6382e09c70ca95b.png?resizew=157)
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