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如图，在平面直角坐标系xOy中，△OAB的顶点A在x轴正半轴上，OC是△OAB的中线，点B，C在反比例函数y＝<img height="35" src="/uploads/meth/20210408/a15fd9cc1efb242611f3d22fe4b0260e.png" width="13" />（x＞0）的图象上，则△OAB的面积等于　   　． 
                                                                                                                                    <img height="129" src="/uploads/meth/20210408/1f012631b7b1f807df95e7b723ea85da.png" width="159" />

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解：作BD⊥x轴于D，CE⊥x轴于E， 
<img height="129" src="/uploads/meth/20210408/46f3ccdb956a66873cfdea3270358243.png" width="159" /> 
∴BD∥CE， 
∴<img height="35" src="/uploads/meth/20210408/f240aaeac3ae12a831582a83dc1b2c57.png" width="21" />＝<img height="35" src="/uploads/meth/20210408/7be764235b232b38b5d0be837eb066fe.png" width="21" />＝<img height="35" src="/uploads/meth/20210408/3e0028e14eda1e57f43fbed9803d503c.png" width="21" />， 
∵OC是△OAB的中线， 
∴<img height="35" src="/uploads/meth/20210408/a6fac7884323bc61601f41f4c68a7161.png" width="21" />＝<img height="35" src="/uploads/meth/20210408/5b972b8732a4cd1f6e4f07ed8dd343ce.png" width="21" />＝<img height="35" src="/uploads/meth/20210408/6473c63c9bbdb49d2dcb34a4731b11c3.png" width="21" />＝<img height="35" src="/uploads/meth/20210408/2a940f975b741f9ecfa6417e6147d11d.png" width="13" />， 
设CE＝x，则BD＝2x， 
∴C的横坐标为<img height="35" src="/uploads/meth/20210408/9f33f8f6f7cf0502359bdf401b347135.png" width="13" />，B的横坐标为<img height="35" src="/uploads/meth/20210408/101b786fdbc418d6d673114432fe69ce.png" width="21" />， 
∴OD＝<img height="35" src="/uploads/meth/20210408/3cabdc35af886432d46f3ec30b55c74f.png" width="21" />，OE＝<img height="35" src="/uploads/meth/20210408/355db65847010dda1d4b0da6bbd412e6.png" width="13" />， 
∴DE＝<img height="35" src="/uploads/meth/20210408/fcf9d811f4d06e479ea8e93ad7e6d358.png" width="13" />﹣<img height="35" src="/uploads/meth/20210408/e93d192972abb98dc8c14333c1e76ff5.png" width="21" />＝<img height="35" src="/uploads/meth/20210408/e1c7040d0428dfa1fdb005e5c921f92d.png" width="21" />， 
∴AE＝DE＝<img height="35" src="/uploads/meth/20210408/4df3c3f8214d1bcf89014d33d2616925.png" width="21" />， 
∴OA＝<img height="35" src="/uploads/meth/20210408/540849385568fce4cb00eeb56fbdde5a.png" width="13" />+<img height="35" src="/uploads/meth/20210408/591b7da390e87a0654f0b276b511604d.png" width="21" />＝<img height="35" src="/uploads/meth/20210408/9cae3d06e7f2a82a0b3ba121dc3fffdb.png" width="21" />， 
∴S△OAB＝<img height="35" src="/uploads/meth/20210408/90e27bbbb19170c96e16ca35eb2d5d12.png" width="13" />OA•BD＝<img height="35" src="/uploads/meth/20210408/acf92074d7966ea7f01a7cf81551d136.png" width="13" />×<img height="35" src="/uploads/meth/20210408/cf69ad0d1fb4e751b725d770b2a50106.png" width="21" />×2x＝<img height="35" src="/uploads/meth/20210408/782ca72c69d4c224a40b4592ede1b037.png" width="13" />． 
故答案为<img height="35" src="/uploads/meth/20210408/65efc694f3677332e95910a066fb9f11.png" width="13" />．

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