2018 AMC 8 第 4 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。
4.
图中的十二边形画在 的方格纸上。该图形的面积是多少 ？
The twelve-sided figure shown has been drawn on graph paper. What is the area of the figure in
小提示：
可以把图形放进一个便于计算的长方形中，或者把它分成中间的正方形和周围的小三角形
Enclose the figure in an easy rectangle or split it into a central square and small triangles.
大提示：
斜边部分形成四个全等的直角三角形，每个面积为
The slanted parts form four congruent right triangles of area .
视频讲解：
Click to load, then click again to play
文字解答：
如图所示，可以把图形分解：
现在可以看出，中间是一个 正方形，周围有 个较小的阴影三角形。
正方形面积为 。每个小三角形的底为 ，高为 ，所以面积为 这样的三角形有 个，所以它们的总面积为 。
因此总面积是 。
所以正确答案是 C。
To solve for the area of the figure, we separate the compound shape into parts that are easier to work with, as such:
As is now clear, there is the center square, with smaller shaded triangles surrounding it.
The area of the square is The other triangles each have a base of and a height of so their area is equal to There are of these triangles, so their total area is
Therefore, the total area is
Thus, the correct answer is C.
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