2025 AMC 8 第 10 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
10.
下图中， 是一个矩形，边长 英寸， 英寸。矩形 顺时针旋转 ，旋转中心是边 的中点，得到第二个矩形。两个重叠矩形覆盖的总面积是多少平方英寸？
In the figure below, is a rectangle with sides of length inches and inches. Rectangle is rotated clockwise around the midpoint of side to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles?
小提示：
把两个矩形面积相加，再减去重叠面积
Add the two rectangle areas and subtract the overlap
大提示：
重叠部分是一个边长为 英寸边一半的正方形
The overlap is a square whose side is half of the -inch side
视频讲解：
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文字解答：
最直接的方法是用容斥：把两个矩形的面积相加，再减去重叠的正方形面积。
每个矩形面积为 。
重叠部分是边长 的正方形，面积为 。
因此总覆盖面积为 ，选 D。
The easiest way to solve this problem is using the Inclusion-Exclusion formula. That is: add the areas of the two rectangles, and then subtract the overlapping (square) area.
Each rectangle has area
Their overlap is a square that has side length and so its area is
Therefore, the total area is which is choice D.
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