Question

一个单位六角星由一个边长为 $1$ 的正六边形和它的 $6$ 个等边三角形延伸部分组成，如图所示。延伸部分的面积与原正六边形面积之比是多少？

A unit hexagram is composed of a regular hexagon of side length $1$ and its $6$ equilateral triangular extensions, as shown in the diagram. What is the ratio of the area of the extensions to the area of the original hexagon?

$1:1$

$6:5$

$3:2$

$2:1$

$3:1$

答案：A

知识点：面积比等边三角形

难度评级：1150

解答：

可以把六边形分成 $6$ 个全等等边三角形，如下图。

因为每个内部三角形都与一个外侧三角形共边，所以所有这些三角形全等。因此面积比为 $1:1$ 。

所以正确答案是 A。

Note that we can split the hexagon into $6$ congruent equilateral triangles as follows.

Since each of them share an edge with an exterior triangle, all the triangles are congruent. Therefore, the ratio of areas is $1:1.$

Thus, A is the correct answer.

2007 AMC 8 第 12 题

答案：A

难度评级：1150

解答：

其他年份的第 12 题