题目内容
(2007•娄底)如图,△ABC是边长为6cm的等边三角形,被一平行于BC的矩形所截,AB被截成三等分,则图中阴影部分的面积为( )![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_ST/images0.png)
A.4cm2
B.2cm2
C.3
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_ST/0.png)
D.3cm2
【答案】分析:由题意知EFGH为等腰梯形,要求它的面积,只要求出EH、FG及高(为等边三角形的高的
)即可.
解答:解:∵等边三角形,被一平行于BC的矩形所截,AB被截成三等分,
∴EH=
BC=2cm,FG=
BC=4cm,且四边形EHGF是等腰梯形,它的高为等边三角形的高的
,
∵等边三角形的高=6×sin60°=3
,
∴等腰梯形高等于
,
∴等腰梯形的面积=
×
=3
,即阴影部分的面积为3
.
故选C.
点评:本题利用了:①等边三角形的性质;②平行线等分线段的性质;③等边三角形高与边长的关系;④梯形的面积公式求解.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/0.png)
解答:解:∵等边三角形,被一平行于BC的矩形所截,AB被截成三等分,
∴EH=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/1.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/3.png)
∵等边三角形的高=6×sin60°=3
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/4.png)
∴等腰梯形高等于
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/5.png)
∴等腰梯形的面积=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/6.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/7.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/8.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231743463725719/SYS201310212317434637257002_DA/9.png)
故选C.
点评:本题利用了:①等边三角形的性质;②平行线等分线段的性质;③等边三角形高与边长的关系;④梯形的面积公式求解.
![](http://thumb2018.1010pic.com/images/loading.gif)
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