2003 AMC 8 第 25 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。
25.
图中，正方形 的面积为 。四个较小正方形边长为 cm，边要么与大正方形的边平行，要么重合。在 中，，且当 沿边 折叠时，点 与 （正方形 的中心）重合。 的面积是多少平方厘米？
In the figure, the area of square is The four smaller squares have sides cm long, either parallel to or coinciding with the sides of the large square. In and when is folded over side point coincides with the center of square What is the area of in square centimeters?
小提示：
设 为 的中点
Let be the midpoint of
大提示：
折叠说明 到 的距离等于 到 的距离
Folding makes the distance from to equal the distance from to
解答：
正方形 的边长为 cm，因为 。
到 的距离是 ，因为它等于 个单位正方形的边长之和。
最后， 到 的距离等于 到 的距离，即
现在可求 ：
因此 的面积为
所以正确答案是 C。
The side length of is cm, since
We also know that the distance from to is since it is the sum of the side lengths of unit squares.
Finally, the distance from to is the same as the distance from to which is
Now, we can find which is
Therefore, the area of is
Thus, C is the correct answer.
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