如图,在△ABC中,DC=2BD,AE=EB,如果△ABC的面积等于a那么阴影部分的面积为多少?

连接BF,做辅助线,有S△AEF=S△ABF/2,S△CDF=S△BFC*2/3,S△ACE=a/2,则S△AFC=a/2-S△AEF,又S△ABF+S△BFC+S△AFC=a,则带入有2S△AEF+S△CDF*3/2+a/2-S△AEF=a,解出有S△AEF+S△CDF*3/2=a/2,又S△ADC=a2/3,S△AFC=S△ADC-S△CDF=a2/3-S△CDF,则△CDF与△AEF有关系如下：a2/3-S△CDF=a/2-S△AEF,解出S△CDF=a/6+S△AEF,带入方程S△AEF+S△CDF*3/2=a/2中,解出S△AEF=a/10,则S△CDF=a4/15,阴影部分面积为S△AEF+S△CDF=a/10+a4/15=11a/30

连接BF，S△AEF=S△ABF/2,S△CDF=S△BFC*2/3，S△ACE=a/2，S△AFC=a/2-S△AEF，S△ABF+S△BFC+S△AFC=a，2S△AEF+S△CDF*3/2+a/2-S△AEF=a，S△AEF+S△CDF*3/2=a/2，又S△ADC=a2/3，S△AFC=S△ADC-S△CDF=a2/3-S△CDF，a2/3-S△CDF=a/2-S△AEF，解出S△CDF=...