Question

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 $4$ 乘 $4$ 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 $4$ -by- $4$ grid is covered by the star?

$40$

$50$

$60$

$75$

$80$

答案：B

知识点：面积对称性

难度评级：720

视频讲解：

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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。

在左上四分之一区域中，移动一个三角形后，可见阴影面积正好占该四分之一区域的一半。

因此星形覆盖了整个网格的 $50\%$ 。正确答案是 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 $50\%,$ which is choice B.

2025 AMC 8 第 1 题

答案：B

难度评级：720

视频讲解：

文字解答：

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