Question

下列四个大的全等正方形分别被分成若干个全等三角形或长方形，并有部分区域被涂阴影。阴影面积占总面积的百分之多少？

Each of the following four large congruent squares is subdivided into combinations of congruent triangles or rectangles and is partially shaded. What percent of the total area is partially shaded?

$12 \dfrac{1}{2}$

$20$

$25$

$33 \dfrac{1}{3}$

$37 \dfrac{1}{2}$

答案：C

知识点：面积分数

难度评级：960

小提示：

四个阴影部分合起来正好等于一个大正方形

The four shaded pieces combine to exactly one large square.

大提示：

将每个阴影部分表示成一个大正方形面积的分数

Express each shaded part as a fraction of one large square.

解答：

左上和右下的阴影区域各占所在正方形的四分之一。右上占八分之一，左下占八分之三。它们的总面积为 $\dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{3}{8} = 1\text{。}$

因此阴影区域合起来等于一个正方形的面积，占四个正方形总面积的 $25 \%$ 。

所以正确答案是 C。

The top left and the bottom right shaded regions are both a quarter of each square. The top right is one-eighth, and the bottom left is three-eighths. Their combined area is $\dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{3}{8} = 1.$

Therefore, the shaded regions combined equal the area of one square, so they are $25 \%$ of the total area.

Thus, C is the correct answer.

2011 AMC 8 第 7 题

答案：C

难度评级：960

小提示：

大提示：

解答：

其他年份的第 7 题