2025 AMC 8 第 1 题
先试着解答 2025 AMC 8 第 1 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2025 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
1.
下图所示的八角星是一种流行的拼布图案。这个星形覆盖了整个 乘 网格的百分之多少？
The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire -by- grid is covered by the star?
小提示：
利用对称性，只看网格的四分之一
Use symmetry to focus on one quarter of the grid
大提示：
比较该四分之一区域内的阴影和非阴影面积
Compare the shaded and unshaded areas inside that quarter
视频讲解：
Click to load, then click again to play
文字解答：
图形具有对称性，所以整个正方形中被星形覆盖的比例，等于任意一个四分之一区域中被覆盖的比例。
只看左上四分之一区域。设想把其中一个三角形平移一下：题目中的阴影面积与下图中的阴影面积完全相同（下图中左上四分之一用粗线标出）：
这样就能一眼看出左上四分之一区域恰好有一半被涂上阴影，所以答案是 ，即选项 B。
There is symmetry, and so whatever fraction of the top-left quarter is shaded, is the same as the fraction of the entire square that is shaded.
Focus on the top-left quarter. Consider moving a single triangle. The shaded area in the problem is exactly the same as the shaded area in this diagram (and the top-left quarter is outlined in bold):
But then it is obvious that exactly half of the top-left quarter is shaded, and so the answer is which is choice B.
其他年份的第 1 题
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