Question

图中形状称为三叶形，由围绕全等等边三角形的边画圆形扇形构成。若三叶形的水平底边长为 $2$ ，它的面积是多少？

The figure shown is called a trefoil and is constructed by drawing circular sectors about sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length $2?$

$\dfrac{1}{3}\pi + \dfrac{\sqrt{3}}{2}$

$\dfrac{2}{3}\pi$

$\dfrac{2}{3}\pi + \dfrac{\sqrt{3}}{4}$

$\dfrac{2}{3}\pi + \dfrac{\sqrt{3}}{3}$

$\dfrac{2}{3}\pi + \dfrac{\sqrt{3}}{2}$

答案：B

知识点：扇形面积分割等边三角形

难度评级：1460

解答：

底边长 $2$ 等于两个半径，所以半径为 $1$ 。这个三叶形由四个等边三角形和四个圆弧段组成，它们可以重新拼成四个半径为 $1$ 、圆心角为 $60^\circ$ 的扇形，总面积为 $4 \cdot \dfrac{60}{360}\pi (1)^2 = \dfrac{2}{3}\pi$ 。

所以正确答案是 B。

Since the base $2$ equals two radii, the radius is $1.$ The trefoil is made of four equilateral triangles and four circular segments, which reassemble into four $60^\circ$ sectors of a circle of radius $1.$ Their total area is $4 \cdot \dfrac{60}{360}\pi (1)^2 = \dfrac{2}{3}\pi.$

Thus, the correct answer is B.

2005 AMC 10A 第 12 题

答案：B

难度评级：1460

解答：

其他年份的第 12 题