如图,长方形ABCD的面积为48,E,F分别在BC,CD上,并且BE=FD=2,求△AFE的面积 如图:长方形ABCD中,E、F分别在BC、CD上,BE=11...
\u5982\u56fe\uff0c\u957f\u65b9\u5f62ABCD\u7684\u9762\u79ef\u4e3a48\uff0eE\uff0cF\u5206\u522b\u5728BC\uff0cCD\u4e0a\uff0c\u5e76\u4e14BE=FD=2\uff0c\u90a3\u4e48\u25b3AEF\u7684\u9762\u79ef\u662f______\u8bbe\u957f\u4e3ax\uff0c\u5bbd\u4e3ay\uff0c\u7531\u9898\u610f\u53ef\u77e5\u25b3AEF\u7684\u9762\u79ef=S\u25a1ABCD-S\u25b3ABE-S\u25b3ECF-S\u25b3ADF\uff0c=48-x-y-\uff08x-2\uff09\uff08y-2\uff09\u00f72\uff0c=48-xy\u00f72-2\uff0c\u2235\u957f\u65b9\u5f62ABCD\u7684\u9762\u79ef\u4e3a48\uff0c\u5373xy=48\uff0c\u2234\u25b3AEF\u7684\u9762\u79ef\u4e3a48-24-2=22\uff0e\u6545\u7b54\u6848\u4e3a\uff1a22\uff0e
\u8bbeAB=a\uff0cAD=b\uff0c\u5219CE=b-11\uff0cCF=a-11\uff0c\u56e0\u4e3a\u77e9\u5f62ABCD\u7684\u9762\u79ef=\u4e09\u89d2\u5f62ABE\u7684\u9762\u79ef+\u4e09\u89d2\u5f62CEF\u7684\u9762\u79ef+\u4e09\u89d2\u5f62AEF\u7684\u9762\u79ef+\u4e09\u89d2\u5f62ADF\u7684\u9762\u79ef\uff0c\u6240\u4ee5ab=1/2\u00d711a+1/2\uff08b-11\uff09\uff08a-3\uff09+17+1/2\u00d73b\uff0c\u6574\u7406\u5f97ab=67\uff0c\u6240\u4ee5\u77e9\u5f62ABCD\u7684\u9762\u79ef=ab=67
解:设长为x,宽为y,由题意可知△AEF的面积=S□ABCD-S△ABE-S△ECF-S△ADF,=48-x-y-(x-2)(y-2)÷2,
=48-xy÷2-2,
∵长方形ABCD的面积为48,即xy=48,
∴△AEF的面积为48-24-2=22.
故答案为:22.
此题可设长为x,宽为y,△AEF的面积可用长方形的面积减去3个小三角形的面积即可求得答案.
解:设长为x,宽为y,由题意可知△AEF的面积=S□ABCD-S△ABE-S△ECF-S△ADF,
=48-2*x-(y-2)*(x-2)-y*(x-2)
=48-xy÷8-8,
∵长方形A0CD的面积为48,即xy=48,
∴△AEF的面积为48-84-8=88.
故答案为:88.
希望可以帮到你
绛旓細8x5梅2=20骞虫柟鍘樼背 闃村奖闈㈢Н 20-4=16骞虫柟鍘樼背 璇峰ソ璇 濡傛灉浣犺鍙垜鐨勫洖绛旓紝鏁鍙婃椂閲囩撼锛寏濡傛灉浣犺鍙垜鐨勫洖绛旓紝璇峰強鏃剁偣鍑汇愰噰绾充负婊℃剰鍥炵瓟銆戞寜閽畘~鎵嬫満鎻愰棶鐨勬湅鍙嬪湪瀹㈡埛绔彸涓婅璇勪环鐐广愭弧鎰忋戝嵆鍙倊浣犵殑閲囩撼鏄垜鍓嶈繘鐨勫姩鍔泘~O(鈭鈭)O锛岃寰楀ソ璇勫拰閲囩撼锛屼簰鐩稿府鍔 ...
绛旓細濡備笅鍥撅紝闀挎柟褰BCD琚垎鎴愪袱涓暱鏂瑰舰锛屼笖AB锛欰E=4:1锛屽浘闃村奖閮ㄥ垎涓夎褰鐨勯潰绉负4骞虫柟鍒嗙背锛岄暱鏂瑰舰ABCD鐨勯潰绉槸锛 锛夊钩鏂瑰垎绫炽備笉鏄疉B锛欰E=4:1鍚э紒闀挎柟褰CDF鐨勯潰绉=8骞虫柟鍒嗙背闀挎柟褰EFB鐨勯潰绉=AB*AE=8AE/CE 骞虫柟鍒嗙背 闀挎柟褰BCD鐨勯潰绉=闀挎柟褰CDF鐨勯潰绉+闀挎柟褰EFB鐨勯潰绉 ...
绛旓細鈭礢闀=ab=30cm^2 鈭碆C=30/4=7.5cm 鎹嬀鑲″畾鐞,寰楋細AC=鈭氾紙4^2+7.5^2锛=8.5cm 涓嶆噦鍙互缁х画闂,
绛旓細鈭礢鈻矱FD=4,S螖CDE=6 鈭碋F:EC=4:6=2:3 鍙堚埖BC鈭F 鈭碊E:BE=EF:EC=2:3 鈭碨螖DEC:S螖BEC=DE:BE=2:3 S螖BEC=9 S鍥涜竟褰ABCD=2(6+9)=30 S鍥涜竟褰BEF=30-4-6-9=11cm^2
绛旓細瑙o細鍥犱负ABCD涓虹煩褰 鎵浠anDAC=CD/AD=3/4 tanEAC=tanBAC=BC/AB=4/3 鎵浠 tanEAD =(tanEAC-tanDAC)/(1+tanEAC*tanDAC)=(4/3-3/4)/(1+4/3*3/4)=(7/12)/2 =7/24 鎵浠F/AE=7/24 EF=7/6*3=7/8 鍥犱负瑙扙=90搴 鎵浠F^2=AE^2+EF^2 EF^2=3^2+(7/8)^2 EF^2...
绛旓細闈㈢Н鏄40鍜岄潰绉槸100鐨闀挎柟褰,瀹界浉绛,闈㈢Н鐨勬瘮绛変簬瀹冧滑闀跨殑姣=m:n 闈㈢Н鏄60鍜岄潰绉槸?鐨勯暱鏂瑰舰,瀹界浉绛,闈㈢Н鐨勬瘮绛変簬瀹冧滑闀跨殑姣=m:n 锛40鍜60涓棿鐨勭嚎娈垫槸m,100鍜?涓棿鐨勭嚎娈垫槸n锛40:100=60:=60脳100梅40 =150
绛旓細鎴戝お杩熶簡 鐢ㄥ皬鍙锋潵绛斿惂 浠F=1锛屼簬鏄疌F=CE=BE=2 浜庢槸AB=CD=DF+FC=1+2=3 AD=BC=BE+EC=2+2=4 浜庢槸闀挎柟褰㈤潰绉=3脳4=12 鈻矨FD=1脳4梅2=2 鈻矨BE=3脳2梅2=3 鈻矯EF=2脳2梅2=2 浜庢槸鈻矨EF=闀挎柟褰-鈻矨FD-鈻矨BE-鈻矯EF=12-2-3-2=5 涔熷氨鏄闀挎柟褰㈤潰绉槸12鐨勬椂鍊欙紝鈻矨EF闈㈢Н鏄5...
绛旓細鏈鐨勫叧閿槸 鍏堝皢FE锛孍C鍒嗗埆鐪嬩綔鏄柍FED鍜屸柍CED鍚勮嚜鐨勫簳杈癸紝D鏄叕鍏遍《鐐癸紝鍒欎袱涓笁瑙掑舰鐨勫競閲岀浉绛夌殑锛岄兘鏄 鐐笵 鍒 CF 鐨勫瀭绾挎锛屽悓鐞嗭紝鈻矯ED鍜屸柍CEA鐨勯珮鏄《鐐笴鍒癇D鐨勫瀭绾挎锛屼篃鐩哥瓑銆傚悓鏃垛柍DEC鈭解柍DCB锛岃孯t鈻矰CB=Rt鈻矪AD锛孲鈻BEF=S鈻矪AD-S鈻矲ED 瑙o細鍥犱负 ED=ED锛屾墍浠 EF鈭禘C=S...
绛旓細濡傚浘锛岄暱鏂瑰舰ABCD鍒嗘垚涓や釜闀挎柟褰紝AB锛欰E=4锛1锛岄槾褰遍儴鍒闈㈢Н涓4骞虫柟鍒嗙背锛岄暱鏂瑰舰ABCD鐨勯潰绉槸锛 10骞虫柟鍒嗙背 锛
绛旓細杩嘑浣淔H鈭D浜E浜嶩銆傗埖FH鈭E銆丆F锛滲F锛屸埓FH鏄柍BCE涓笌CE骞宠鐨勪腑浣嶇嚎锛屸埓FH锛滶C/2銆傗埖DE鈭禘C锛1鈭3锛屸埓锛圖E锛婨C锛/EC锛濓紙1锛3锛/3锛屻鈭碋C锛3DC/4銆傗埖ABCD鏄姝鏂瑰舰锛鈭碊C鈭B銆丏C锛滱B銆丄B鈯F銆傗埓FH锛滶C/2锛濓紙3DC/4锛/2锛3AB/8銆傜敱DC鈭B銆丗H鈭D锛屽緱锛欻F鈭B锛屸埓...