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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">解：在图中标上字母，令<i>AB</i>与<i>A</i>′<i>D</i>′的交点为点<i>E</i>，过<i>E</i>作<i>EF</i>⊥<i>AC</i>于点<i>F</i>，如图所示．</span></span></span></span></span><br />
<img height="195" src="/uploads/meth/20210402/3b8c7dbf9e697353298fb7c52f2fa386.png" width="204" /><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∵四边形<i>ABCD</i>为菱形，<i>AB</i>＝2，∠<i>BAD</i>＝60°，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴∠<i>BAO</i>＝30°，∠<i>AOB</i>＝90°，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴<i>AO</i>＝<i>AB</i>•cos∠<i>BAO</i>＝</span></span></span></span></span><img height="18" src="/uploads/meth/20210402/00789b457d871f2df9df0727b73fddef.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，<i>BO</i>＝<i>AB</i>•sin∠<i>BAO</i>＝1．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">同理可知：<i>A</i>′<i>O</i>＝</span></span></span></span></span><img height="18" src="/uploads/meth/20210402/fbbde60b20fcc57bed974c69a7b10468.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，<i>D</i>′<i>O</i>＝1，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴<i>AD</i>′＝<i>AO</i>﹣<i>D</i>′<i>O</i>＝</span></span></span></span></span><img height="18" src="/uploads/meth/20210402/0d95069b42663dfe0d4d265661926ded.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">﹣1．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∵∠<i>A</i>′<i>D</i>′<i>O</i>＝90°﹣30°＝60°，∠<i>BAO</i>＝30°，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴∠<i>AED</i>′＝30°＝∠<i>EAD</i>′，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴<i>D</i>′<i>E</i>＝<i>AD</i>′＝</span></span></span></span></span><img height="18" src="/uploads/meth/20210402/be937d6efcab62e0233de0a403778616.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">﹣1．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">在Rt△<i>ED</i>′<i>F</i>中，<i>ED</i>′＝</span></span></span></span></span><img height="18" src="/uploads/meth/20210402/8dfeb70d6c62e6fc01dad6f731e2036a.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">﹣1，∠<i>ED</i>′<i>F</i>＝60°，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴<i>EF</i>＝<i>ED</i>′•sin∠<i>ED</i>′<i>F</i>＝</span></span></span></span></span><img height="37" src="/uploads/meth/20210402/ddfc9e62b02985054ff3fcf0d0485931.png" width="41" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴<i>S</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">阴影</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">＝<i>S</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">菱形<i>ABCD</i></span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">+4<i>S</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">△<i>AD</i>′<i>E</i></span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210402/81cf097543f5b185d3855731130bf6ed.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">×2<i>AO</i>×2<i>BO</i>+4×</span></span></span></span></span><img height="35" src="/uploads/meth/20210402/e276a9fb0586d6d92e5c6fdf5926dc04.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span style="line-height:150%"><span style="font-family:宋体">AD</span></span></i><span style="line-height:150%"><span style="font-family:宋体">′•<i>EF</i>＝6</span></span></span></span></span><img height="18" src="/uploads/meth/20210402/3a9dc2d6856b0655b41f91701abbe02f.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">﹣6．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">故答案为：6</span></span></span></span></span><img height="18" src="/uploads/meth/20210402/6c05f43ed869bbd83f773a7c55ea1f91.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">﹣6．</span></span></span></span></span>

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