【题目】如图，把边长为1的正方形ABCD绕顶点A逆时针旋转30°到正方形AB′C′D′，则它们的公共部分的面积等于_____．

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参考答案：

【答案】

【解析】连接AW，如图所示：

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根据旋转的性质得：AD=AB′，∠DAB′=60°，

在Rt△ADW和Rt△AB′W中，

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∴Rt△ADW≌Rt△AB′W（HL），

∴∠B′AW=∠DAW=[Failed to download image : http://qbm-images.oss-cn-hangzhou.aliyuncs.com/QBM/2012/4/10/1573365777752064/1573365848252416/EXPLANATION/e26123d7027d4671a513b601eaf7a446.png]

又AD=AB′=1，

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