如图,△ABC的面积为1,BD=½DC,AF=½FD,CE=½EF,求DEF的面积.class="ikqb_img" src="http://h.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=46c4ea2db7fd5266a77e34129b28bb13/e1fe9925bc315c60f3a78d298cb1cb13485477c2.jpg" esrc="htt
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![如图,△ABC的面积为1,BD=½DC,AF=½FD,CE=½EF,求DEF的面积.class=](/uploads/image/z/1646890-34-0.jpg?t=%E5%A6%82%E5%9B%BE%2C%E2%96%B3ABC%E7%9A%84%E9%9D%A2%E7%A7%AF%E4%B8%BA1%2CBD%EF%BC%9D%26%23189%3BDC%2CAF%EF%BC%9D%26%23189%3BFD%2CCE%EF%BC%9D%26%23189%3BEF%2C%E6%B1%82DEF%E7%9A%84%E9%9D%A2%E7%A7%AF.class%3D%22ikqb_img%22+src%3D%22http%3A%2F%2Fh.hiphotos.baidu.com%2Fzhidao%2Fwh%253D600%252C800%2Fsign%3D46c4ea2db7fd5266a77e34129b28bb13%2Fe1fe9925bc315c60f3a78d298cb1cb13485477c2.jpg%22+esrc%3D%22htt)
如图,△ABC的面积为1,BD=½DC,AF=½FD,CE=½EF,求DEF的面积.class="ikqb_img" src="http://h.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=46c4ea2db7fd5266a77e34129b28bb13/e1fe9925bc315c60f3a78d298cb1cb13485477c2.jpg" esrc="htt
如图,△ABC的面积为1,BD=½DC,AF=½FD,CE=½EF,求DEF的面积.
class="ikqb_img" src="http://h.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=46c4ea2db7fd5266a77e34129b28bb13/e1fe9925bc315c60f3a78d298cb1cb13485477c2.jpg" esrc="http://h.hiphotos.baidu.com/zhidao/wh%3D450%2C600/sign=ce2b78ee962bd4074292dbf94eb9b267/e1fe9925bc315c60f3a78d298cb1cb13485477c2.jpg" />
如图,△ABC的面积为1,BD=½DC,AF=½FD,CE=½EF,求DEF的面积.class="ikqb_img" src="http://h.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=46c4ea2db7fd5266a77e34129b28bb13/e1fe9925bc315c60f3a78d298cb1cb13485477c2.jpg" esrc="htt
△ABD和△ACD高相等,都为A到BC的距离,因此面积比等于底边比
所以S△ABD:S△ACD=BD:CD=1:2
所以S△ACD为S△ABC的2/3,面积为2/3
△ACF和△DCF高相等,都为C到AD的距离
所以S△ACF:S△DCF=AF:DF=1:2
所以S△CDF为S△ACD的2/3,为2/3×2/3=4/9
△CDE和△FDE高相等,因此面积比等于底边比
S△DEF:S△CDE=CE:EF=1:2
所以S△DEF为S△CDF的2/3,为4/9×2/3=8/27