Question

图中显示了瓷砖地板的一个角。如果整个地板都按这种方式铺设，并且四个角都像这个角一样，那么较深色瓷砖占整个瓷砖地板的几分之几？

A corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like this one, then what fraction of the tiled floor is made of darker tiles?

$\dfrac{1}3$

$\dfrac{4}9$

$\dfrac{1}2$

$\dfrac{5}9$

$\dfrac{5}8$

答案：B

知识点：铺砖面积比

难度评级：1580

解答：

注意有重复的 $3 \times 3$ 区域，并且具有相同图案（可能旋转方向不同）。

在这个区域中，有三个单位正方形，还有两个三角形合起来形成另一个单位正方形。

因此深色区域面积为 $4$ ，整个区域面积为 $9$ 。所求分数为 $\dfrac{4}{9}$ 。

所以正确答案是 B。

Notice that there are repeating $3 \times 3$ regions with the same pattern (they might be rotated differently).

In this region, there are three unit squares, and two triangles that combine to form another unit square.

This makes the area of the darker region $4$ and the whole region $9.$ The desired fraction is then $\dfrac{4}{9}.$

Thus, B is the correct answer.

2002 AMC 8 第 23 题

答案：B

难度评级：1580

解答：

其他年份的第 23 题