Question

如图， $8 \times 18$ 的矩形 $ABCD$ 被切成两个全等的六边形，使这两个六边形可以无重叠地重新拼成一个正方形。求 $y$ ？

The $8 \times 18$ rectangle $ABCD$ is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is $y?$

$6$

$7$

$8$

$9$

$10$

答案：A

知识点：面积正方形（几何）

难度评级：1310

解答：

两个六边形组成一个面积为 $8 \cdot 18 = 144$ 的正方形，所以正方形边长为 $12$ 。

阶梯形切线把宽分成三个长度为 $y$ 的相等水平部分，它们合起来跨过整个宽度： $y + y + y = 18$ ，所以 $y = 6$ 。（两个竖直台阶各上升 $12 - 8 = 4$ ，形成正方形多出的高度。）

因此，正确答案是 A。

The two hexagons form a square of area $8 \cdot 18 = 144,$ so the square has side $12.$

The staircase cut splits the width into three equal horizontal pieces of length $y,$ which together span the full width: $y + y + y = 18,$ so $y = 6.$ (The two vertical steps each rise $12 - 8 = 4,$ building the extra height of the square.)

Thus, the correct answer is A.

2006 AMC 12A 第 6 题

答案：A

难度评级：1310

解答：

其他年份的第 6 题