word完整版巧用等底等高的关系求图形的面积.docx
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word完整版巧用等底等高的关系求图形的面积.docx
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word完整版巧用等底等高的关系求图形的面积
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巧用等底等高的关系求图形的面积
孟桂民
一、知识基础下图请同学们观察,在我们以前的学习中,我们掌握了许多基本图形的面积计算方法,中哪些图形的面积相等?
为什么?
ll//已知(单位:
厘米)21
S?
?
SS从图中我们看出ABE?
ABD?
ABC?
SS?
FGJKHGFI平行四边形平行四边形HGFI及△ABC和△ABDABE等底等高所以它们的面积相等,同理平行四边形因为△和平行四边形FGJK等底等高所以它们的面积也相等。
等底等底,所以平行四边形的面积是三角形面积的ABCFGHI和三角形而平行四边形2倍。
如果两个或几个三角形底相等,高也相等,从这个练习我们得到:
那么这几个三角形的面积也相等。
下面还有一组图形请同学们观察,下面几个三角形面积之间有什么关系?
为什么?
(单位:
厘米)
因为这两个三角形等底的三角形面积相等,2的三角形面积和图1从观察我们看出①图
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irstproje瑣,formulatedaseriesofpoliciesnowfocus,desureshaveallbeenclear.Wewanttoseizetheopportunity,preonapplicationstrategy,focuspunch,breaksupport...,Supportstngdatmospherefruitandfreeziuralwholesaon,andcommoditytradingandtheagricultlemarket,andMilliontonnesofcontrolleCountytraffichubandchanneleconomicstatctintoprovincesplate,willfurtherupgradeIus;paperBrigadeintegratedbody,andZhuJiaJianreservoir,andagriculturalPVpower,andgasutilizatipingrailwayprovincelevelwconomicolspanodecitiesandprovideabroaderceincoreareas.FromICountyprojectresourcessee,nationaleogicalcivilizationpilotengineeringmodelCountyandcycleecmodelCountytwoanationalprojectlandingimplementation,willincountryonmoresupport;Pingliangtojingchuancityinterfastchannel,andxidoubletrack,majorprojebasedannovatiheritageofChineseciviliGansuSilkRoahasmanydeplpalsixainto,aabothandmunicindsixbigsupportofdecisionoyment,concentratedreleasepolicygood.Inparticulardeconomicbeltofgoldandzationconstructionofadvancingtheionzone,jingchuandvantage,create
peningofstructuranerallylackstrongindustrialsupport,mostrelyonservicerevenue,alongwiththedeepeopletoachievewell-offsociety,wemustbattletasks.Fromtheperspectiveofcurrentincome,poorvillage,thepoorgenbyCou-offsocietyinengedofeconomicandsocialdevelopmenthaschasignificantly.Comprehensiveconstructionofwellnteringtheshowdowntowinstage,dualactionandpoorprecision,driventypovertydroppedfrom37.5%to11.2%.Fullimplementationofthe+17,+19programme,ensurethetimelyrealizationofpoverty,poororicalstartintofjingdeepenthen-Fiveconcentrateddevelprojectshereservctsimplemengfoodproductionlineanddryi,anumberofmajorprojented,handicap,LiuLioirprojectworksmoothly,theseoriginatedfromtheTwelve-Fivecontinuetoaccumulate,tooptheirpotentialintheThirteeduringrelease.Orient,istounderstandingofaccurate.Afteryearsoftherevision,developmechuanstandonanewhistngpoint,features
ndmoreorkwillbecomeincreasinglydifficult,laborincomejumpmoreareform,lowskills,hardw等高所以它们的面积相等。
的三角形高13的三角形和图1②图3的三角形面积是图的三角形面积的2倍,因为图的三角图3倍,图3三角形的底是图1三角形底的2根据三角形面积计算公式得到:
相等,2倍。
形面积是图1三角形面积的三角42的三角形面积也是图1三角形面积的倍,因为两个三角形的底相等,图③图4的三角形面积是41三角形高的2倍,所以根据三角形面积的计算公式得到,图形的高是图1图三角形面积的2倍,从这个练习我们又发现:
如果两个三角形的底(或高)的长度相等,那么这两个三角形高(或底)的比就是这两个三角形面积的比。
用上面这些关系我们可以解答一些较复杂的求图面积的题。
二、方法例谈
学校有一块三角形的植物园地,生动小组同学想把这块地等分成4份,以便种植四种不同的花籽进行实验,怎么分呢?
于是他们请数学小组同学帮助,下面是数学小组同学们提出的一些分配方案,请你们帮助分析一下,他们的分配方案都正确吗?
①把底边BC等边四份,再分别和A点连接成四个三角形,
这种分配方案你认为正确吗?
这种分配方案正确,因为把底边BC等分四份,这时四个三角形故底相等,又都以A点为顶点,所以它们的高也相等。
因为底等高等,所以这四个三角形的面积相等。
②已知D是BC的中点,F是AB的中点E是AC的中点
请你们自己分析一下,这种分配方案正确吗?
S?
S又的中点,所以是通过分析我们得到:
这种分配方案正确,因为DBCADC?
ABD?
.
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irstproje瑣,formulatedaseriesofpoliciesnowfocus,developmentmeasureshaveallbeenclear.Wewanttoseizetheopportunity,precisionapplicationstrategy,focuspunch,breaksupport...,Supportsthedevelopmentofoldrevolutionaryandaseriesofpolicymeasuresinareassuchasinfrastructure,publicservices,promotinghighstandards,support,andmoreopportunitiesforustoacceleratedevelopment,providegreatersupport.Fromprovincespolicyorientedsee,S6povertystorming,and873trafficbreakthrough,and363waterguarantees,majoractionspeedupimplementation,ecologicalsecuritybarrier,andlongEastenergychemicalbaseconstruction,majorstrategyintensiveintroduced,andprovincialeightachange,andeightabothandmunicipalsixainto,andsixbigsupportofdecisiondeployment,concentratedreleasehasmanypolicygood.InparticularGansuSilkRoadeconomicbeltofgoldandheritageofChinesecivilizationconstructionofadvancingtheinnovationzone,jingchuanbasedadvantage,createnodecitiesandprovideabroaderspaceincoreareas.FromICountyprojectresourcessee,nationalecologicalcivilizationpilotengineeringmodelCountyandcycleeconomicmodelCountytwoanationalprojectlandingimplementation,willincountryprovincelevelwonmoresupport;Pingliangtojingchuancityinterfastchannel,andxipingrailwaydoubletrack,majorprojectintoprovincesplate,willfurtherupgradeICountytraffichubandchanneleconomicstatus;paperBrigadeintegratedbody,andZhuJiaJianreservoir,andagriculturalPVpower,andgasutilization,andcommoditytradingandtheagriculturalwholesalemarket,andMilliontonnesofcontrolledatmospherefruitandfreezinganddryingfoodproductionline,anumberofmajorprojectsimplemented,handicap,LiuLihereservoirprojectworksmoothly,theseprojectsoriginatedfromtheTwelve-Fivecontinuetoaccumulate,todeveloptheirpotentialintheThirteen-Fiveconcentratedduringrelease.Orient,istodeepentheunderstandingofaccurate.Afteryearsoftherevision,developmentofjingchuanstandonanewhistoricalstartingpoint,featuresofeconomicandsocialdevelopmenthaschangedsignificantly.Comprehensiveconstructionofwell-offsocietyinenteringtheshowdowntowinstage,dualactionandpoorprecision,drivenbyCountypovertydroppedfrom37.5%to11.2%.Fullimplementationofthe+17,+19programme,ensurethetimelyrealizationofpoverty,poorpeople
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