AMC 8 2025 Problem 10
AMC8 2025 年第 10 题
面积与周长（综合）★★☆☆☆
In the figure below, is a rectangle with sides of length AB = 5 inches and AD = 3 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?
如图所示，ABCD是一个长方形，其边长AB = 5英寸，AD = 3英寸。长方形ABCD绕DC边的中点顺时针旋转90°，得到第二个长方形。请问这两个重叠长方形覆盖的总面积是多少平方英寸？
- A.21
- B.22.25
- C.23
- D.23.75
- E.25
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
The area of each rectangle is . Then the sum of the areas of the two regions is the sum of the areas of the two rectangles, minus the area of their overlap. To find the area of the overlap, we note that the region of overlap is a square, each of whose sides have length 2.5 (as they are formed by the midpoint of one of the long sides, the vertex, and also, since it is rotated 90 degrees). Then the answer is .
~ cxsmi, Srinjini 060313
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