Question

阴影区域由两个互相垂直相交的矩形组成，尺寸如图所示。它的面积是多少平方单位？

The shaded area is formed by two intersecting perpendicular rectangles, with dimensions as shown. Its area, in square units, is

$23$

$38$

$44$

$46$

无法由给定信息确定

unable to be determined from the information given

答案：B

知识点：面积容斥原理

难度评级：960

解答：

水平矩形面积为 $10 \times 2 = 20$ ，竖直矩形面积为 $3 \times 8 = 24$ 。它们的重叠部分是一个 $3 \times 2$ 矩形，面积为 $6$ 。

直接相加两个矩形会把重叠部分算两次，所以阴影面积是 $20 + 24 - 6 = 38$ 。

所以正确答案是 B。

The horizontal rectangle has area $10 \times 2 = 20,$ and the vertical rectangle has area $3 \times 8 = 24.$ Their overlap, a $3 \times 2$ rectangle, has area $6.$

Adding the two rectangles counts the overlap twice, so the shaded area is $20 + 24 - 6 = 38.$

Thus, the correct answer is B .

1988 AMC 8 第 17 题

答案：B

难度评级：960

解答：

其他年份的第 17 题