2006 AMC 8 第 5 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。
5.
点 、、 和 是大正方形各边的中点。如果大正方形面积为 ，小正方形的面积是多少？
Points and are midpoints of the sides of the larger square. If the larger square has area what is the area of the smaller square?
小提示：
小正方形周围的四个角三角形全等。
The four corner triangles around the smaller square are congruent.
大提示：
那四个外侧三角形可重新排列覆盖小正方形。
Those four outside triangles can be rearranged to cover the smaller square.
解答：
可以把所有三角形向内折叠，正好覆盖小正方形。这说明小正方形的面积是大正方形面积的一半。
所以小正方形面积为 。
所以正确答案是 D。
Note that we can fold all the triangles in to perfectly cover the smaller square. This means that area of the smaller square is half the area of the larger square.
This makes the area of the smaller square
Thus, D is the correct answer.
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