如图，正方形ABCD、正方形BEFG和正方形RKPF的边长分别为a、b、c，点G在线段DK上，则图中阴影部分的面积为 （2014?新泰市一模）三个正方形ABCD，BEFG，RKP...
\u6b63\u65b9\u5f62ABCD\u3001\u6b63\u65b9\u5f62BEFG\u548c\u6b63\u65b9\u5f62RKPF\u7684\u4f4d\u7f6e\u5982\u56fe\u6240\u793a\uff0c\u70b9G\u5728\u7ebf\u6bb5DK\u4e0a\uff0c\u6b63\u65b9\u5f62BEFG\u7684\u8fb9\u957f\u4e3a4\uff0c\u5219\u25b3DEK\u7684\u9762D \u8fde\u63a5DB\u3001GE\u3001FK\uff0c\u5219DB\u2225GE\u2225FK\uff0c\u518d\u7531\u5e73\u884c\u7ebf\u95f4\u7684\u8ddd\u79bb\u76f8\u7b49\u53ca\u540c\u5e95\u7b49\u9ad8\u7684\u4e24\u4e09\u89d2\u5f62\u9762\u79ef\u76f8\u7b49\u5f97\u51faS \u25b3 DGE =S \u25b3 GEB \uff0cS \u25b3 GKE =S \u25b3 GFE \uff0c\u8fdb\u800c\u628a\u9634\u5f71\u90e8\u5206\u9762\u79ef\u8f6c\u5316\u4e3a\u6b63\u65b9\u5f62GBEF\u7684\u9762\u79ef\uff0c\u5373S \u9634\u5f71 =S \u6b63\u65b9\u5f62GBEF \uff0e\u89e3\uff1a\u5982\u56fe\uff0c\u8fde\u63a5DB\u3001GE\u3001FK\uff0c\u5219DB\u2225GE\u2225FK\uff0c \u5728\u68af\u5f62GDBE\u4e2d\uff0cS \u25b3 DGE =S \u25b3 GEB \uff08\u540c\u5e95\u7b49\u9ad8\u7684\u4e24\u4e09\u89d2\u5f62\u9762\u79ef\u76f8\u7b49\uff09\uff0c\u540c\u7406S \u25b3 GKE =S \u25b3 GFE \uff0e\u2234S \u9634\u5f71 =S \u25b3 DGE +S \u25b3 GKE \uff0c=S \u25b3 GEB +S \u25b3 GEF \uff0c=S \u6b63\u65b9\u5f62GBEF \uff0c=4\u00d74=16\u6545\u9009D\uff0e
\u89e3\uff1a\u8bbeAB=a\uff0cFP=b\uff0c\u5ef6\u957fPK\uff0cBE\u4ea4\u4e8e\u70b9M\uff0c\u2235\u56db\u8fb9\u5f62ABCD\u4e3a\u6b63\u65b9\u5f62\uff0c\u2234AB=AD=CD=BC=a\uff0c\u2234S\u25b3AED=12\uff084+a\uff09a\uff0c\u2235CG=BC-BG=a-4\uff0c\u2234S\u25b3CGD=12\uff08a-4\uff09a\uff0c\u2235\u56db\u8fb9\u5f62FPRK\u4e3a\u6b63\u65b9\u5f62\uff0c\u2234FR=RK=PK=FP=b\uff0c\u2235GF=4\uff0c\u2234S\u25b3KPG=12\uff084+b\uff09b\uff0c\u2235\u56db\u8fb9\u5f62FEBG\u3001FPKR\u4e3a\u6b63\u65b9\u5f62\uff0c\u2234\u2220MBG=\u2220BGP=\u2220P=90\u00b0\uff0c\u2234\u77e9\u5f62FPME\uff0c\u2234PM=4 KM=4-b\uff0c\u2235EM=b\uff0c\u2234S\u25b3EKM=12\uff084-b\uff09b\uff0c\u2234S\u25b3DKE=\uff08S\u6b63\u65b9\u5f62ABCD+S\u6b63\u65b9\u5f62GFEB+S\u77e9\u5f62FPME\uff09-\uff08S\u25b3AED+S\u25b3CGD+S\u25b3GPK+S\u25b3EMK\uff09\uff0c=\uff08a2+42+4b\uff09-[12\uff084+a\uff09a+12\uff08a-4\uff09a+12\uff084+b\uff09b+12\uff084-b\uff09b]\uff0c=a2+16+4b-[2a+12a2+12a2-2a+2b+12b2+2b-12b2]=a2+16+4b-[a2+4b]=16\uff1b\u89e3\u6cd5\u4e8c\u3001\u8fde\u63a5BD\u3001GE\u3001FK\uff0c\u5219\u6839\u636e\u6b63\u65b9\u5f62\u6027\u8d28\u63a8\u51fa\u2220PFK=\u2220FGE=\u2220CDB=45\u00b0\uff0c\u5373BD\u2225GE\u2225FK\uff0c\u5219\u6839\u636e\u7b49\u5e95\u7b49\u9ad8\u7684\u4e09\u89d2\u5f62\u9762\u79ef\u76f8\u7b49\u5f97\u51fa\uff1aS\u25b3GED=S\u25b3GBE\uff0cS\u25b3KGE=S\u25b3FEG\uff0c\u2234\u9634\u5f71\u90e8\u5206\u7684\u9762\u79ef\u662fS=S\u25b3GED+S\u25b3KEG=S\u25b3GEB+S\u25b3FGE=S\u6b63\u65b9\u5f62BGFE=16\uff1b\u6545\u9009B\uff0e
如图，连BD、GE、FK，则DB ∥ GE ∥ FK，
在梯形DBEG中，S △GED =S △GEB ，
同理可得，S △GEK =S △GEF ，
∴S 阴影 =S △GED +S △GEK ，
=S △GEB +S △GEF ，
=S 正方形BEFG ，
∵正方形BEFG的边长为b，
∴S 阴影 =b 2 ．
故答案为：b 2 ．
绛旓細鈭 涓や釜姝ｆ柟褰鐨勯潰绉垎鍒负10鍜3 鈭 涓や釜姝ｆ柟褰㈢殑杈归暱鍒嗗埆涓衡垰10鍜屸垰3 S闃村奖=鐭╁舰AEHD锛堝欢闀緿C鍜孍F 鐩镐氦浜嶩锛-锛圫鈻矨BD+S鈻矰FH+S鈻矪EF锛=AD*AE-[锛圓D*AB锛+锛圖H*FH锛+锛圔E*EF锛塢/2 =鈭10*锛堚垰10+鈭3锛-[鈭10 ²+锛堚垰10+鈭3 锛夛紙鈭10+鈭3锛+鈭3²]/2 =锛10...
绛旓細10脳10梅2锛=100梅2锛=50锛堝钩鏂瑰帢绫筹級锛涚瓟锛氫笁瑙掑舰BFD鐨勯潰绉负50骞虫柟鍘樼背锛
绛旓細CGE = BEG - BEC = b²/2 - ab/2 = b(b - a) / 2 DEG = CDE + CDG + CGE = (a² + ab - a² + b² - ab)/ 2 = b² / 2
绛旓細鎴戜滑鏉ヨ瘉鏄庝竴鑸儏褰:浠E=1,AB=k.鈻矨BG鈮屸柍CBE,鏄撹瘉AH鈯E.浣淏P鈯E浜嶱.鍒橞P鈭H.鈻矨HE鈭解柍ABG,AH:HE=AB:BG=AB:BE=k:1,鐭B涓衡垹AHB鐨勮骞冲垎绾.BH=鈭2BP.(杩欎釜搴旇鏄棰樺叧閿偣)AH:AE=AB:AG,鐭H=k(k+1)/鈭(1+k^2),AH:BP=AE:BE,鐭P=k/鈭(1+k^2),BH=鈭2BP=鈭2...
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绛旓細S=S锛ABCD锛+S锛圔EFG锛-S锛圓EF锛-S锛圓DC锛=a^2+b^2-a^2/2-(a+b)*b/2 =锛坅^2+b^2)/2-ab/2 褰揳=5鍘樼背锛宐=3鍘樼背鏃 s=(25+9)/2-1/2*5*3 =17-7.5 =9.5
绛旓細1 2 a 2 - 1 2 ab- 1 2 b 2 = 1 2 锛坅 2 +b 2 -ab锛= 1 2 [锛坅+b锛 2 -3ab]锛屽綋a+b=17锛宎b=60鏃讹紝S 闃村奖 = 1 2 脳锛289-180锛=54.5锛庢晠绛旀涓猴細54.5 ...
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