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【321407】【详解】6年级_下册_第08讲_几何综合练习

时间:2025-01-08 19:51:20 作者: 字数:3414字
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第八讲 几何综合练习

  1. 答案:21.解答:设AOD面积为1份,则AOB面积为2份,COD面积为6份,BOC面积为12份,阴影部分面积为13份,说明每份面积就是1平方厘米,所以四边形ABCD面积等于21份,是21平方厘米.

  2. 答案:18解答: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,所以三角形ADC的面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

  3. 答案: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> 解答: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,所以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,所以乙的长宽比为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

  4. 答案:24.解答:连接IC,则ICDF平行.所以三角形DFI的面积等于三角形DFC的面积,即 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

  5. 答案:41.12.解答:如图1,阴影部分的面积等于等腰直角三角形ABC的面积加上一个半圆,即 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

  6. 答案:17.875.解答:如图2,阴影部分面积等于梯形ABCD的面积减去一个四分之一圆的面积,即 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

  7. 答案:2880.解答:锯开后,表面积中增加了8个长方形截面,因此每个截面面积为12平方厘米,木料原来的体积是 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> 立方厘米.

  8. 答案:194.解答:从前后、左右、上下方向看,求出各方向所能看到的面积再相加即可: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

  9. 答案:90.解答:如图3,作DN垂直于MFN,由 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,得 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,从而阴影部分面积为等腰直角三角形AGM面积的5倍: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

  10. 答案:244.解答:如图4,直角三角形OAB的三边长之比 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,且斜边 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,所以两直角边分别长1216,长方形的长和宽分别为3212,所以阴影部分面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

Shape1


  1. 答案:40.解答:设三角形 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> 面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,由 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,故三角形 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> 面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ;又由 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,可设三角形CBEBEF的面积分别为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,于是左边面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,右边面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,可得 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,三角形ADG的面积为40

  2. 答案:58.解答:如图5,作EF垂直BCF.则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,所以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,五边形面积等于三角形ABE面积加上梯形BEDC面积,即 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

  3. 答案:15.6.解答:如图6,设丙三角形的边长为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,则:
     <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>
     <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,得: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,解得: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

Shape3

  1. 答案:2487.解答:翻转问题中,不动的点为圆心.点A的翻滚路线如图7中的选线所示,路线长为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> .翻滚过程中,正三角形所扫过的区域包含两个圆心角是120°的扇形以及一个等边三角形,面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

  2. 答案:(11.29;(2388.8.解答:(1)要使水面高度最小,则面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> 平方厘米的侧面应该贴地,此时水面情况如图8所示,水面高度等于三角形ABC的高线AD的一半.因为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,所以水面高度为1.2.而要使水面高度最大,应使面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> 平方厘米的底面贴地,由于水占总体积的 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,因而此时水面高度为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>
    2)这一问难度极大,需要学生有很深的几何功底.注意到三个侧面分别贴地时,所对应的三个水面高度恰好与直角三角形的三边成反比,而对于 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,只有302418满足勾股定理,所以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> 即为三棱柱底面直角三角形的三边比.由于底面积是54,所以底面的三边分别为91215,总的侧面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,所以三棱柱的高为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>
    接下来比较 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> 的底面贴地与 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> 的侧面贴地这两种情况,水面高度比为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,设两高度分别为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> .以容器中水的体积为等量关系,可列出等式: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,求得 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,所以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> ,所以容器中水的体积是 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/272/" title="几何" class="c1" target="_blank">几何</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a>

Shape4

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