在△ABC中, AB、BC、AC三边的长分别为
、
、
,求这个三角形的面积.小华同学在解答这道题时,先画一个正方形网格(每个小正方形的边长为1),再在网格中画出格点△ABC(即△ABC三个顶点都在小正方形的顶点处),如图1所示.这样不需求△ABC的高,而借用网格就能计算出它的面积.这种方法叫做构图法.
(1)△ABC的面积为: .
(2)若△DEF三边的长分别为
、
、
,请在图2的正方形网格中画出相应的
△DEF,并利用构图法求出它的面积为_____________.
(3)如图3,△ABC中,AG⊥BC于点G,以A为直角顶点,分别以AB、AC为直角边,向△ABC外作等腰Rt△ABE和等腰Rt△ACF,过点E、F作射线GA的垂线,垂足分别为P、Q.试探究EP与FQ之间的数量关系,并证明你的结论.
(4)如图4,一个六边形的花坛被分割成7个部分,其中正方形PRBA,RQDC,QPFE的面积分别为13m2、25m2、36m2,则六边形花坛ABCDEF的面积是 m2.
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/c72f520681574db2b263afa38d5c6848.png)
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/2d19fc19c1814c989f034bf33a386fca.png)
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/03beec85fff240cfa83289995cdbd28a.png)
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/3510b6530e7d4a68b04a6b0e299e97cb.png)
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/c5df79f306f0483d8ab12d6006235f9a.png)
(1)△ABC的面积为: .
(2)若△DEF三边的长分别为
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/5cbfcda94bb6497d8822106f6bb8803e.png)
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/ec06f837adf34870b85d972ecd9316fb.png)
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/5f7f407348534823aa9758d2190b5711.png)
△DEF,并利用构图法求出它的面积为_____________.
(3)如图3,△ABC中,AG⊥BC于点G,以A为直角顶点,分别以AB、AC为直角边,向△ABC外作等腰Rt△ABE和等腰Rt△ACF,过点E、F作射线GA的垂线,垂足分别为P、Q.试探究EP与FQ之间的数量关系,并证明你的结论.
(4)如图4,一个六边形的花坛被分割成7个部分,其中正方形PRBA,RQDC,QPFE的面积分别为13m2、25m2、36m2,则六边形花坛ABCDEF的面积是 m2.
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/c72f520681574db2b263afa38d5c6848.png)
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/2d19fc19c1814c989f034bf33a386fca.png)
![](https://img.xkw.com/dksih/QBM/2014/12/12/1573768704950272/1573768710602752/STEM/e8f2840d4255439f9340647243febbb6.png)
更新时间:2016-12-05 21:43:32
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