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【321145】【详解】六年级(上)第08讲 复杂直线形计算仅答案

时间:2025-01-08 19:31:42 作者: 字数:3455字
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第八讲 复杂直线型计算

例题:

  1. 答案:16厘米
    详解:长方形的长为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,宽为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .再根据长比宽多8厘米,就能求出 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> 厘米.长方形A中,阴影部分的周长为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .长方形B中,阴影部分有6条边,它的周长其实就等于大长方形的周长,等于 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .两者相差 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> 厘米.

  2. 答案: <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a>
    详解:因为△CDF是正三角形,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> 正五边形的内角和是 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,每个内角是 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .因此 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .△BCF是等腰三角形,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,同理 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> 也等于 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .因此看得到 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a>

  3. 答案:22
    详解:如图连接AM,因为PMAD,所以由蝴蝶模型可知三角形DFP与三角形AFM面积相等;同样道理三角形BEN与三角形AEM面积相等,所以三角形BEN面积=4321=22



    Shape1

  4. 答案:30
    详解:三角形AFE与三角形DCE构成沙漏模型,而已知面积比为4:9,所以对应边长比为EF:EC=2:3,因此FE:FC=2:5.三角形AFE又与三角形BFC构成金字塔模型,所以三角形AFE与三角形BFC的面积比为4:25,因此三角形BFC的面积为25,所以四边形ABCE的面积为254=21,因此平行四边形的面积为21+9=30

  5. 答案:15
    详解: <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .由此可得, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .而 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,因此阴影部分的面积等于 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a>

  6. 答案:30
    详解:三角形ABF与三角形DEF构成沙漏模型,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,即 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,又因为AD=12,所以AF=6,因此 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .所以三角形CFE的面积= <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a>


练习:

  1. 答案:90
    简答:阴影部分的外周长与大正六边形相同,而阴影部分的外周长等于内周长的3倍,因此阴影部分外周长等于总周长的 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,即 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a>

  2. 答案: <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a>
    简答:四边形内角等于90°,五边形内角等于108°,六边形内角等于120°,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .△AFK与△AHK都是等腰三角形,因此 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,两者相差 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a>

  3. 答案:25
    简答:如图作辅助线构造蝴蝶模型即可.



    Shape2

  4. 答案:36
    简答:三角形AOD与三角形BOC构成沙漏模型,而已知面积比为4:16=1:4,所以对应边长比为OD:OB=1:2,因此三角形AOD与三角形BOA的面积比为1:2,所以三角形BOA的面积为8.由蝴蝶模型可知三角形COD的面积也是8,所以梯形的面积是4+16+8+8=36

作业:

  1. 答案:270
    简答:设小长方形的长为x,宽为y.从水平方向的线段可以看出 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> ,因此 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .所以小长方形的长宽比为3:2,而相应小正方形的边长就是 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> 份.由此可得小长方形的面积是白色小正方形的 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> 倍,即 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a> .接着把小长方形与小正方形的面积相加即可得到答案.

  2. Shape3 案:75°
    简答:如右图,添加一个点F.△ADE是正三角形,所以Shape4 ,因此Shape5 ,由于△AFE是由△BFE折叠而来的,因此两个三角形完全相同,都是直角三角形,而且Shape6 .因此Shape7


  3. 答案:24
    简答:由Shape8 ,得:Shape9 Shape10 .又由Shape11 ,得Shape12 ,所以整个长方形的面积为24


  4. 答案:1
    简答:不妨设Shape13 .由EFAB平行,得Shape14
    所以Shape15 Shape16  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/78/" title="直线" class="c1" target="_blank">直线</a> <a href="/tags/222/" title="复杂" class="c1" target="_blank">复杂</a>
    Shape17 ,所以Shape18 ,阴影部分面积为Shape19


  5. 答案:Shape20
    简答:AD:AB=1:3由金字塔模型可知Shape21 .在三角形ADO与三角形EFO中由沙漏模型可知DO:OE=AD:EF,而由金字塔模型可知EF:AB=2:3,所以DO:OE=AD:EF=1:2,因此Shape22 ,因此三角形ADO的面积为Shape23

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