AMC 8 2007 Problem 12
AMC8 2007 年第 12 题
四边形与多边形★★★☆☆
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?
一个单位六角星由一个边长为 1 的正六边形及其 6 个等边三角形形状的凸出部分组成，如图所示。则凸出部分的总面积与原来六边形的面积之比是多少？
- A.1:1
- B.6:5
- C.3:2
- D.2:1
- E.3:1
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
The six equilateral triangular extensions fit perfectly into the hexagon meaning the answer is
Split the hexagon into six small equilateral triangles. You will see that the six outer triangles can be folded to the hexagon, so the answer is 1:1.
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