问题
解答题
在平面上，七个边长均为1的等边三角形，分别用①至⑦表示（如图）．从④⑤⑥⑦组成的图形中，取出一个三角形，使剩下的图形经过一次平移，与①②③组成的图形拼成一个正六边形．
（1）你取出的是哪个三角形？写出平移的方向和平移的距离．
（2）将取出的三角形任意放置在拼成的正六边形所在平面上，问：正六边形没有被三角形盖住时面积能否等于
？请说明理由．
答案
解：（1）当取出的是⑦时，将剩下的图形向上平移1（如图1）；
当取出的是⑤时，将⑥⑦向上平移2（如图2）；
（2）能．理由如下：
每个小等边三角形的面积为
，
五个小等边三角形的面积和为
，
正六边形的面积为
，
而
<
<
，
所以正六边形没有被三角形盖住的面积能等于
．
图1
图2
完形填空
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