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

<<

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
完形填空。
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