小升初复习：阴影部分求面积及周长(含答案)

【史上最全小学求阴影部分面积专 题 快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题 —含答案】 小学及小升初复习专题-圆与求阴影部分面积 ----完整答案在最后面 目标:通过专题复习，加强学生对于图形面积计算的灵活运用。并加深对面积和周长概念的理解和区分。面积求解大致分为以下几类: c 重难点:观察图形的特点，根据图形特点选择合适的方法求解图形的面积。能灵活运用所学过的基本的平面图形的面积求阴影部分的面积。 例2.正方形面积是7平方厘米，求阴影部分的面积。 例1.求阴影部分的面积。 (单位:厘米) (单位:厘米) 例3.求图中阴影部分的面积。(单位:厘米) 例4.求阴影部分的面积。(单位:厘米) 例5.求阴影部分的面积。(单位:厘米) 例6.如图:已知小圆半径为2厘米，大圆半径是小圆的3倍， 问:空白部分甲比乙的面积多多少厘 米, 例7.求阴影部分的面积。(单位:厘米) 例8.求阴影部分的面积。(单位:厘米) temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 例9.求阴影部分的面积。(单位:厘米) 例10.求阴影部分的面积。(单位:厘米) 例11.求阴影部分的面积。(单位:厘米) 例12.求阴影部分的面积。(单位: 厘米) 例13.求阴影部分的面积。(单位:厘米) 例14.求阴影部分的面积。(单位:厘米) 例16.求阴影部分的面积。(单位:厘米) 例15.已知直角三角形面积是12平方厘米，求阴影部分的面 积。 temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 例17.图中圆的半径为5厘米,求阴影部分的面积。(单位:厘米) 例18.如图，在边长为6厘米的等边三角形中挖去三个同样的 扇形,求阴影部分的周长。 例19.正方形边长为2厘米，求阴影部分的面积。 例20.如图，正方形ABCD的面积是36平方厘米，求阴影部 分的面积。 例21.图中四个圆的半径都是1厘米，求阴影部分的面积。 例22. 如图，正方形边长为8厘米，求阴影部分的面积。 例23.图中的4个圆的圆心是正方形的4个顶点，，它们的公例24.如图，有8个半径为1厘米的小圆，用他们的圆周的一共点是该正方形的中心，如果每个圆的半径都是1厘米，那部分连成一个花瓣图形，图中的黑点是这些圆的圆心。如果么阴影部分的面积是多少,圆周π率取3.1416，那么花瓣图形的的面积是多少平方厘 米, temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and3/11 neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 例25.如图，四个扇形的半径相等，求阴影部分的面积。(单位:例26.如图，等腰直角三角形ABC和四分之一圆DEB，AB=5厘米) 厘米，BE=2厘米，求图中阴影部分的面积。 例27.如图，正方形ABCD的对角线AC=2厘米，扇形ACB例28.求阴影部分的面积。(单位:厘米) 是以AC为直径的半圆，扇形DAC是以D为圆心，AD为半 径的圆的一部分，求阴影部分的面积。 例29.图中直角三角形ABC的直角三角形的直角边AB=4厘例30.如图，三角形ABC是直角三角形，阴影部分甲比阴影米，BC=6厘米，扇形BCD所在圆是以B为圆心，半径为BC部分乙面积大28平方厘米，AB=40厘米。求BC的长度。 的圆，?CBD=，问:阴影部 分甲比乙面积小多少, 例31.如图是一个正方形和半圆所组成的图形，其中P为半圆例32.如图，大正方形的边长为6厘米，小正方形的边长为周的中点，Q为正方形一边上的中点，求阴影部分的面积。 4厘米。求阴影部分的面积。 temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 例33.求阴影部分的面积。(单位:厘米) 例34.求阴影部分的面积。(单位:厘米) 例35.如图，三角形OAB是等腰三角形，OBC是扇形，OB=5 厘米，求阴影部分的面积。 举一反三?巩固练习 专1 】下图中，大小正方形的边长分别是9厘米和5厘米，求阴影部分的面积。 【 【专1-1】.右图中，大小正方形的边长分别是12厘米和10厘米。求阴影部分面积。 temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and5/11 neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 【专1-2】. 求右图中阴影部分图形的面积及周长。 【专2】已知右图阴影部分三角形的面积是5平方米，求圆的面积。 【专2-1】已知右图中，圆的直径是2厘米，求阴影部分的面积。 【专2-2】求右图中阴影部分图形的面积及周长。 【专2-3】 求下图中阴影部分的面积。(单位:厘米) 【专3】求下图中阴影部分的面积。 temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 【专3-1】求右图中阴影部分的面积。 【专3-2】求右图中阴影部分的面积。 【专3-3】求下图中阴影部分的面积。 temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and7/11 neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 完整答案 例1解:这是最基本的方法: 圆面积减去等腰直角三角形例2解:这也是一种最基本的方法用正方形的面积减去 圆的面积， 的面积。 设圆的半径为 r，因为正方形的面积为7平方厘米，所以 ×-2×1=1.14(平方厘米) =7， 所以阴影部分的面积为:7-=7-×7=1.505平方厘米 例4解:同上，正方形面积减去圆面积， 例3解:最基本的方法之一。用四个 圆组成一个圆，用正 16-π()=16-4π 方形的面积减去圆的面积， =3.44平方厘米 所以阴影部分的面积:2×2-π,0.86平方厘米。 例5解:这是一个用最常用的方法解最常见的题，为方便起例6解:两个空白部分面积之差就是两圆面积之差(全加上见， 阴影部分) 我们把阴影部分的每一个小部分称为“叶形”，是用两个圆 π-π()=100.48平方厘米 减去一个正方形， (注:这和两个圆是否相交、交的情况如何无关) π()×2-16=8π-16=9.12平方厘米 另外:此题还可以看成是1题中阴影部分的8倍。 例7解:正方形面积可用(对角线长×对角线长?2，求) 例8解:右面正方形上部阴影部分的面积，等于左面正方形 正方形面积为:5×5?2=12.5 下部空白部分面积，割补以后为圆， 所以阴影面积为:π?4-12.5=7.125平方厘米 所以阴影部分面积为:π()=3.14平方厘米 (注:以上几个题都可以直接用图形的差来求,无需割、补、 增、减变形) 例9解:把右面的正方形平移至左边的正方形部分，则阴影例10解:同上，平移左右两部分至中间部分，则合成一个长部分合成一个长方形， 方形， 所以阴影部分面积为:2×3=6平方厘米 所以阴影部分面积为2×1=2平方厘米 (注: 8、9、10三题是简单割、补或平移) 例11解:这种图形称为环形，可以用两个同心圆的面积差或例12. 解:三个部分拼成一个半圆面积( 差的一部分来求。 π()?,,14.13平方厘米 (π -π)×=×3.14=3.66平方厘米 例13解: 连对角线后将"叶形"剪开移到右上面的空白部分,凑 例14解:梯形面积减去圆面积， 成正方形的一半. 所以阴影部分面积为:8×8?2=32平方厘米 (4+10)×4-π=28-4π=15.44平方厘米 . 例15. 分析: 此题比上面的题有一定难度,这是"叶形"的一个 半. 例16解:,π，π,π, 解: 设三角形的直角边长为r，则=12，=6 =π(116-36)=40π=125.6平方厘米 圆面积为:π?2=3π。圆内三角形的面积为12?2=6， temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 阴影部分面积为:(3π-6)×=5.13平方厘米 例17解:上面的阴影部分以AB为轴翻转后，整个阴影部分例18解:阴影部分的周长为三个扇形弧，拼在一起为一个半成为梯形减去直角三角形，或两个小直角三角形AED、BCD圆弧， 面积和。 所以圆弧周长为:2×3.14×3?2=9.42厘米 所以阴影部分面积为:5×5?2+5×10?2=37.5平方厘米 例19解:右半部分上面部分逆时针，下面部分顺时针旋转到 例20解:设小圆半径为r，4=36, r=3，大圆半径为R，左半部分，组成一个矩形。 所以面积为:1×2=2平方厘米 =2=18, 将阴影部分通过转动移在一起构成半个圆环, 所以面积为:π(-)?2=4.5π=14.13平方厘米 例21. 解:把中间部分分成四等分，分别放在上面圆的四个例22解法一: 将左边上面一块移至右边上面,补上空白,则左角上，补成一个正方形，边长为2厘米， 边为一三角形,右边一个半圆. 所以面积为:2×2=4平方厘米 阴影部分为一个三角形和一个半圆面积之和. π()?2+4×4=8π+16=41.12平方厘米 解法二: 补上两个空白为一个完整的圆. 所以阴影部分面积为一个圆减去一 个叶形,叶形面积为:π()?2-4×4=8π-16 所以阴影部分的面积为:π()-8π+16=41.12平方厘 米 例24分析:连接角上四个小圆的圆心构成一个正方形，各个例23解:面积为,个圆减去,个叶形，叶形面积为:π 小圆被切去个圆， -1×1=π-1 这四个部分正好合成,个整圆，而正方形中的空白部分合成 所以阴影部分的面积为:4π-8(π-1)=8平方厘米 两个小圆( 解:阴影部分为大正方形面积与一个小圆面积之和( 为:4×4+π=19.1416平方厘米 例25分析:四个空白部分可以拼成一个以,为半径的圆( 例26解: 将三角形CEB以B为圆心，逆时针转动90度，到 所以阴影部分的面积为梯形面积减去圆的面积， 三角形ABD位置,阴影部分成为三角形ACB面积减去个小 4×(4+7)?2-π=22-4π=9.44平方厘米 圆面积, 为: 5×5?2-π?4=12.25-3.14=9.36平方厘米 例28解法一:设AC中点为B,阴影面积为三角形ABD面积例27解: 因为2==4，所以=2 加弓形BD的面积, 以AC为直径的圆面积减去三角形ABC面积加上弓形 三角形ABD的面积为:5×5?2=12.5 AC面积， temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and9/11 neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 弓形面积为:[π?2-5×5]?2=7.125 π-2×2?4+[π?4-2] 所以阴影面积为:12.5+7.125=19.625平方厘米 =π-1+(π-1) 解法二:右上面空白部分为小正方形面积减去小圆面积，其 =π-2=1.14平方厘米 值为:5×5-π=25-π 阴影面积为三角形ADC减去空白部分面积，为:10×5?2- (25-π)=π=19.625平方厘米 例29. 解: 甲、乙两个部分同补上空白部分的三角形后合成一例30. 解:两部分同补上空白部分后为直角三角形ABC，一个扇形BCD，一个成为三角形ABC， 个为半圆，设BC长为X，则 40X?2-π?2=28 此两部分差即为:π×,×4×6,5π-12=3.7平 所以40X-400π=56 则X=32.8厘米 方厘米 例31. 解:连PD、PC转换为两个三角形和两个弓形， 例32解:三角形DCE的面积为:×4×10=20平方厘米 两三角形面积为:?APD面积+?QPC面积= (5×10+5×5)=37.5 梯形ABCD的面积为:(4+6)×4=20平方厘米 从而知道 它们面积相等,则三角形ADF面积等于三角形EBF面积，阴 两弓形PC、PD面积为:π-5×5 影部分可补成圆ABE的面积，其面积为: π?4=9π=28.26平方厘米 所以阴影部分的面积为:37.5+π-25=51.75平方厘 米 例33. 解:用大圆的面积减去长方形面积再加上一个以2为 例34解:两个弓形面积为:π-3×4?2=π-6 半径的圆ABE面积，为 阴影部分为两个半圆面积减去两个弓形面积，结果为 π+π-(π-6)=π(4+-)+6=6平方 (π+π)-6 厘米 =×13π-6 =4.205平方厘米 例35解:将两个同样的图形拼在一起成为圆减等腰直角三 temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive 角形 [π?4-×5×5]?2 =(π-)?2=3.5625平方厘米 举一反三?巩固练习-answer 【专1】(5+9)×5?2+9×9?2,(5+9)×5?2=40.5(平方厘米) 【专1-1】(10+12)×10?2+3.14×12×12?4,(10+12)×10?2=113.04(平方厘米) 【专1-2】面积:6×(6?2),3.14×(6?2)×(6?2)?2=3.87(平方厘米) 周长: 3.14×6?2+6，(6?2)×2=21.42(厘米) 【专2】2r×r?2=5 即r×r=5 圆的面积=3.14×5=15.7(平方厘米) 【专2-1】3.14×(2?2)×(2?2),2×2?2=1.14(平方厘米) 【专2-2】面积:3.14×6×6?4,3.14×(6?2)×(6?2)?2=14.13 (平方厘米) 周长:2×3.14×6?4+3.14×6?2+6=24.84 (厘米) 【专2-3】(6+4)×4?2,(4×4,3.14×4×4?4)=16.56(平方厘米) 【专3】6×3,3×3?2=13.5(平方厘米) 【专3-1】8×(8?2)?2=16(平方厘米) 【专3-2】3.14×4×4?4,4×4?2=4.56(平方厘米) 【专3-3】5×5?2=12.5(平方厘米) temperature piping and equipment, avoid oil pipeline, avoiding vibration equipment, principles of construction of beautiful and11/11 neat easy to install. 5.1.5.2 from field instrumentation and valves field junction boxes to the single line slot cable using pipe, 220VAC power cord shall be full pipe laying, indoor coaxial cables concealed and outdoor wear buried. 5.1.5.3 bending cold bending method should be used to protect pipe, bending angle should not be less than 900, when wearing non-armoured cable and laid, bend radius should not be less than 6 times the pipe diameter, when while wearing armored cable and concealed, bend radius should not be less than 10 times the pipe diameter. Bend protection tube there should be no dents, cracks, single right-angled bend protection tube should not be more than two. 5.1.5.4 between protective tube and between protective tube and connector, threaded connections should be used, it tube end screw thread length should not be less than 1/2 of the fitting, and ensures the electrical connection. 5.1.5.5 protection tube should line up, ... 5.1.7 5.1.7.1 check tubing for pressure piping laying pipe, components, materials and specifications meet the design requirements, and have quality certificates, before laying should be cleared by welding and bending the welding slag, rust, chip or a foreign body, and preservative treatments. 5.1.7.2 in pressure piping welding welder must have a valid welder certificate. 5.1.7.3 tubing under the conditions to meet measurement requirements should be as short as possible, General length should not be more than 15m, pipe bending cold bending, cutting machine, minimizing bending and cross, and there shall be no sharp and complex bending, bending radius of not less than 3 times the pipe diameter. 5.1.7.4 pipe and process equipment, piping, or building surface distance is greater than 50mm, not be laid parallel to the oil, combustible, explosive