2007 AMC 8 第 23 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。
23.
图中 方格里的阴影风车形面积是多少？
What is the area of the shaded pinwheel shown in the grid?
小提示：
从整个方格中减去未阴影面积更容易
It is easier to subtract the unshaded area from the whole grid.
大提示：
未阴影部分由四个角落正方形和四个全等三角形组成
The unshaded part consists of four corner squares and four congruent triangles.
解答：
可以用总面积减去未阴影面积来求阴影面积。
有 个边长为 的正方形，每个面积为 ，对未阴影面积贡献共 。
还有 个底为 、高为 的三角形，总面积为
未阴影总面积为 。
整个方格面积为 ，所以阴影面积为 。
所以正确答案是 B。
We can find the area of the shaded part by subtracting the area of the unshaded part from the whole area.
There are squares with side length contributing each to the unshaded area, for a total of
There are also triangles with base and height This contributes a total area of
The total unshaded area is therefore
The total area is and subtracting the unshaded area yields as the area of the shaded region.
Thus, B is the correct answer.
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