如图，长方形ABCD的面积为120平方厘米，BE=3AE，BF=2FC,求四边形EGFB的面积。
\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u957f\u65b9\u5f62ABCD\u7684\u9762\u79ef\u4e3a120\u5e73\u65b9\u5398\u7c73\uff0cBE=3AE,BF=2FC,\u6c42\u56db\u8fb9\u5f62EGFB\u7684\u9762\u79ef\uff1f\uff1f\u3010\u8003\u70b9\u3011\u4e09\u89d2\u5f62\u9762\u79ef\u4e0e\u5e95\u7684\u6b63\u6bd4\u5173\u7cfb\uff0e
\u3010\u4e13\u9898\u3011\u5e73\u9762\u56fe\u5f62\u7684\u8ba4\u8bc6\u4e0e\u8ba1\u7b97\uff0e
\u3010\u5206\u6790\u3011\u6211\u4eec\u901a\u8fc7\u4e09\u89d2\u5f62\u7684\u76f8\u4f3c\u6c42\u51faEG\u4e0eGD\u7684\u6bd4\uff0c\u8fdb\u4e00\u6b65\u6c42\u51fa\u25b3AED\u7684\u9762\u79ef\uff0c\u518d\u8fd0\u7528\u5927\u25b3ABF\u7684\u9762\u79ef\u51cf\u53bb\u25b3AEG\u7684\u9762\u79ef\u5c31\u662f\u56db\u8fb9\u5f62EGFB\u7684\u9762\u79ef\uff0e
\u3010\u89e3\u7b54\u3011
\u3000\u3000\u89e3\uff1a\u5ef6\u957fDC\u3001AF\u4ea4\u4e8e\u70b9H\uff0c
\u3000\u3000\u56e0\u4e3aABCD\u662f\u957f\u65b9\u5f62\uff0c
\u3000\u3000\u6240\u4ee5AB\u2225DH\uff0c
\u3000\u3000\u6240\u4ee5\u25b3HCF\u223d\u25b3ABF\uff0c\u25b3AEG\u223d\u25b3HDG\uff0c
\u3000\u3000\u5373
\u3000\u3000HC/AB =CF/BF \uff0c
\u3000\u3000AE/DH =EG/GD \uff0c
\u3000\u3000\u56e0\u4e3aBE=3AE\uff0cBF=2FC\uff0c
\u3000\u3000\u6240\u4ee5AE=1/4AB\uff0cCH=1/2 AB\uff0c
\u3000\u3000\u5373AE\uff1aDH=1\uff1a6\uff0c
\u3000\u3000\u6240\u4ee5EG\uff1aGD=1\uff1a6\uff0c
\u3000\u3000\u56e0\u4e3a\u25b3AED\u7684\u9762\u79ef=1/4AE\u00d7AD\u00f72\uff0c
\u3000\u3000\u56e0\u4e3a\u957f\u65b9\u5f62\u7684\u9762\u79ef\u662f120\u5e73\u65b9\u5398\u7c73\uff0c
\u3000\u3000\u6240\u4ee5\u25b3AED=15\u5e73\u65b9\u5398\u7c73\uff0c
\u3000\u3000\u53c8\u56e0\u25b3AEG\u4e0e\u25b3AGD\u7684\u9762\u79ef\u6bd41\uff1a6\uff0c
\u3000\u3000\u25b3AED=15\u00f7\uff086+1\uff09=15/7\uff08\u5e73\u65b9\u5398\u7c73\uff09\uff1b
\u3000\u3000\u53c8\u56e0\u25b3ABF\u7684\u9762\u79ef=2/3BC\u00d7AB\u00f72=2 /3 \u00d7120\u00f72\uff0c=40\uff08\u5e73\u65b9\u5398\u7c73\uff09\uff0c
\u3000\u3000\u56db\u8fb9\u5f62EGBF\u7684\u9762\u79ef=\u25b3ABF-\u25b3AEG=40-15/7=265/7 \uff08\u5e73\u65b9\u5398\u7c73\uff09\uff1b
\u3000\u3000\u5373\u56db\u8fb9\u5f62EGBF\u7684\u9762\u79ef\u662f265/7 \u5e73\u65b9\u5398\u7c73\uff0e
\u3010\u70b9\u8bc4\u3011\u672c\u9898\u8fd0\u7528\u4e86\u4e09\u89d2\u5f62\u7684\u76f8\u4f3c\u53ca\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u516c\u5f0f\uff0c\u8003\u67e5\u4e86\u5b66\u751f\u5206\u6790\uff0c\u89e3\u51b3\u95ee\u9898\u7684\u65b9\u6cd5\u4e0e\u80fd\u529b\uff0e
(53/56)*40
假设AB=4a，BC=3b延长AF，与DC交于H
△ABF与△HCF相似
AB/HC=BF/CF=2
∴HC=2a
HD=4a+2a=6a
△AEG与△HDG相似
△AEG的高：△HDG的高=AE/HD=1/6
△AEG的高=1/7BC=3b/7
△ABF的面积=4a*2b=8ab
△AEG的面积=a*3b/7=3ab/7
四边形的面积=8ab-3ab/7=53ab/7
∵长方形的面积=4a*3b=120
∴ab=10
∴所求四边形的面积=53*10/7
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