高思学校竞赛数学导引——六年级第11讲几何综合二超越篇第8题详解
8．如图15 -30，正方形PQRS有三个顶点分别在三角形ABC的三条边上，且BQ=QC.请求出正方形PQRS的面积．
![](https://wkrtcs.bdimg.com/rtcs/image?w=181.13333333333&md5sum=1cb2c807ca95d8db6ffb2bc9be49cb10&sign=043c64c900&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=41&ipr={"t":"img","w":"181.13333333333","h":"178.66666666667","dataType":"jpeg","c":"word/media/image1.png","imgOriW":565,"imgOriH":559})
![](https://wkrtcs.bdimg.com/rtcs/image?w=180&md5sum=1cb2c807ca95d8db6ffb2bc9be49cb10&sign=043c64c900&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=41&ipr={"t":"img","w":"180","h":"152.66666666667","dataType":"png","c":"word/media/image2.png","imgOriW":430,"imgOriH":364})
图15—31 图15—32
设三角形ABC的面积为1，
如图15—32，15—33，e=1-c-d-(b+![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=1cb2c807ca95d8db6ffb2bc9be49cb10&sign=043c64c900&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=41&ipr={"t":"img","w":"16","h":"41","dataType":"gif","c":"word/media/image4.png"})
),1---=。
a=2e=![](https://wkrtcs.bdimg.com/rtcs/image?w=29&md5sum=1cb2c807ca95d8db6ffb2bc9be49cb10&sign=043c64c900&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=41&ipr={"t":"img","w":"29","h":"41","dataType":"gif","c":"word/media/image8.png"})
×2=,b+c+d=1-a=1-=， =
![](https://wkrtcs.bdimg.com/rtcs/image?w=196.66666666667&md5sum=1cb2c807ca95d8db6ffb2bc9be49cb10&sign=043c64c900&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=41&ipr={"t":"img","w":"196.66666666667","h":"163.33333333333","dataType":"png","c":"word/media/image13.png","imgOriW":571,"imgOriH":475})
![](https://wkrtcs.bdimg.com/rtcs/image?w=180&md5sum=1cb2c807ca95d8db6ffb2bc9be49cb10&sign=043c64c900&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=41&ipr={"t":"img","w":"180","h":"144.66666666667","dataType":"png","c":"word/media/image14.png","imgOriW":483,"imgOriH":388})
图15—33 图15——34
如图15—34，将三角形c和d分别以P、R为中心按逆时针和顺时针方向旋转90度，形成有两个直角三角形APM和ARM连在一起的四边形。此四边形的面积就是b+c+d的面积，b+c+d=7×6÷2+9×2÷2=30,可得a=![](https://wkrtcs.bdimg.com/rtcs/image?w=23&md5sum=1cb2c807ca95d8db6ffb2bc9be49cb10&sign=043c64c900&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=41&ipr={"t":"img","w":"23","h":"41","dataType":"gif","c":"word/media/image12.png"})
×30=27.2(平方厘米)。
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