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1、平面组合图形的面积计算一、教学目标1.初步了解组合图形面积的计算方法，会计算一些较简单的组合图形的面积；2.熟练运用割补（平移、翻转）方法计算组合图形阴影部分的面积。二、教学重、难点重点：利用正方形、长方形、平行四边形、三角形、梯形这些平面图形面积来求组合图形的面积。难点：根据图形特征采用什么方法来分解组合图形，达到分解的图形既明确而又准确求出题目要求的面积。三、教学过程1.复习引入（用字母表示下列面积、周长和体积计算公式）周长公式面积体积正方形正方形正方体长方形长方形长方体圆三角形圆柱半圆圆圆锥扇形扇形梯形：圆柱侧面积：圆柱表面积：2.例题讲解题型一（求组合图形的某一边长或周长）例 1 如图
2、所示，在直角三角形 ABC 中，求斜边 AB 边上的高 CD 的长度（单位：厘米）。解析：此题主要考查同学们对三角形面积的理解，以及灵活运用三角形的面积求三角形中相关的线段。已知直角三角形的三边，可根据等积法求出线段CD 的长度。14362ABCS（平方厘米）6252.4CD（厘米）DCBEA练习一（1）图中，王叔叔上班有两条路可走，他走哪条路近？（2）公园里有一个半圆的花圃，花圃周围要围上竹篱笆，竹篱笆长多少米？题型二（求组合图形的面积）例 2 如图，已知梯形 ABCD 的面积是 560平方厘米，ABCE 是正方形，:5:4CEED。求三角形的面积。解 析：因 为:5:4C EE D，所 以
3、 正 方 形 和 三 角 形的 面 积 比 是25:1 05:2，三角形的面积为25601607（平方厘米）练习二（1）如图，是由 4 个相同的半圆形组合的，已知图形的周长是50.24厘米，求图形的面积。(2)如图所示，长方形的长12 cm，宽 8 cm，DE=5 cm，求 ABC 的面积。题型三（利用平移法求阴影部分面积)10米公司家文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档
4、编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文
5、档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4
6、文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I
7、4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4
8、I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J
9、4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7
10、J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4555555例 3求下图阴影部分的面积。（单位：厘米）解：将阴影部分进行平移，合并成一个简单图形，再求它们的面积，如上右图。552 5（平方厘米）答：阴影部分的面积是25 平方厘米。练习三求下面阴影部分的面积。题型四（利用割补法求阴影部分的面积）例 4 求下图阴影部分的面积。（单位：厘米）解法一把组合图形看成是梯形里包含着扇形、阴影
11、部分和三角形。21111614 10103.14 1014 1024220078.5 7051.5SSSS阴影梯形三角形扇形（平方厘米）解法二把组合图形看成是由扇形、阴影部分和一个直角三角形组成的。211(16 10)3.14 101610104216078.53051.5SSSS阴影长方形三角形扇形（平方厘米）解法三把组合图形只看成扇形与阴影部分的和，而不考虑三角形。2111016103.14 1013078.551.524SSS阴影梯形扇形（平方厘米）答：阴影部分的面积是51.5平方厘米。练习四（1）如图，图中四个等圆的周长都是50.24厘米，求阴影部分的面积。161014105文档编码:
12、CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码
13、:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编
14、码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档
15、编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文
16、档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4
17、文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I
18、4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4（2）如图所示，求阴影部分的面积。例 5 如图所示，阴影甲的面积比阴影乙的面积大2
19、8 平方厘米，AB=40 厘米，BC 垂直于AB，求 BC 的长。解析：要求 BC 的长，关键要求出三角形ABC 的面积，再根据面积公式求解。由图形可知：阴影甲的面积比阴影乙的面积大 28 平方厘米，实际上就是半圆的面积比三角ABC 的面积大 28 平方厘米，因而由半圆的面积可得三角形 ABC 的面积。221402860022ABCScm60024030BCcm练习五如图所示，平行四边形ABCD 的边长 BC=10 厘米，直角三角形BCE 的直角边CE=8 厘米，已知阴影部分的面积比三角形EFG 的面积大 10 平方厘米，求 CF 的长。3.课后练习（1）如图所示，两只小虫同时从点A 出发，以
20、相同的速度向点C 爬行，小虫甲沿甲路爬行，小虫乙沿乙路爬行，到达点 C（填“甲先”，“乙先”，“同时”）。（2）如图所示，弧线从平行四边形的对角处把平行四边形分成了A、B 两部分。比较 A、B 两部分的周长()。A-样长BA 长些C无法比较DB 长些甲乙文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文
21、档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4
22、文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I
23、4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4
24、I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J
25、4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7
26、J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C
27、7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I48CBDA（3）如图所示，是将两个相同的长宽分别等于56与 28 的长方形拼成的图形，求这个图形的周长（单位：厘米）（4）如图所示，长方形ABCD 被虚线分割成 4 个面积相等的部分，其中AE=2，AD=9，试求线段 BE 的长。（5）如图所示，李大爷的一块菜地紧靠着一面墙，在菜地的四周围上木篱笆，留出一条1米宽的门以供出入，已知木篱笆的总长是27 米，如果每平方米收获白菜10 千克，求这块地一共可收获白菜多少千克
28、？（6）如图，已知四边形ABCD 为正方形，边长是10厘米，求阴影部分的面积。（7）如图，已知 AB=BC，且 AB=10 厘米，求阴影部分的面积。CBAD文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG
29、1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:C
30、G1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:
31、CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码
32、:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编
33、码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档
34、编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文
35、档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4S1S2438（8）如图，三角形1S 的面积比三角形2S 的面积大多少平方厘米？（单位：厘米）（9）如图所示，此图形是 20XX 年在北京召开了国际数学家大会的会标。它是由四个相同的直角三角形拼成的，直角三角形的两条直角边分别为3 和 4，求大正方形的面积是多少？（10）右图中，正方形的面积是40 平方厘米，求图中阴影部分的面积。(11)如图所示，在梯形 ABCD 中，OA：OC=3：5，215AOBScm，求梯形 ABCD 的面积。(12)求阴影部分的面积O8文档编码:CG1B4A10X8J1 HB4C10P
36、2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10
37、P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C1
38、0P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C
39、10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4
40、C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB
41、4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4文档编码:CG1B4A10X8J1 HB4C10P2P9U10 ZX7I7C7J4I4