2013 AMC 8 第 24 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。
24.
正方形 、 和 面积相等。点 和 分别是边 和 的中点。阴影五边形 的面积与三个正方形面积之和的比是多少？
Squares and are equal in area. Points and are the midpoints of sides and respectively. What is the ratio of the area of the shaded pentagon to the sum of the areas of the three squares?
小提示：
设每个正方形边长为
Let each square have side length .
大提示：
从总面积 中减去非阴影的长方形和三角形
Subtract the unshaded rectangle and triangle from the total area .
视频讲解：
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文字解答：
设每个正方形边长为 ，则三个正方形总面积为 。从总面积中减去对角线 左侧的非阴影区域会更容易。
根据解答图，长方形 面积为 ，三角形 面积为 因此非阴影面积为 ，阴影五边形面积为 。
所求比值为 。
所以正确答案是 C。
Let each square have side length , so the total area of the three squares is . It is easier to subtract the unshaded region to the left of diagonal from this total.
Using the solution diagram, rectangle has area , and triangle has area Thus the unshaded area is , so the shaded pentagon has area .
The requested ratio is .
Thus, C is the correct answer.
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