Question

在一个 $4$ 乘 $4$ 的正方形外侧，以正方形的四条边为直径作四个半圆。另一个正方形 $ABCD$ 的边分别与原正方形对应边平行，并且 $ABCD$ 的每一边都与一个半圆相切。正方形 $ABCD$ 的面积是

Around the outside of a $4$ by $4$ square, construct four semicircles with the four sides of the square as their diameters. Another square, $ABCD,$ has its sides parallel to the corresponding sides of the original square, and each side of $ABCD$ is tangent to one of the semicircles. The area of the square $ABCD$ is

$16$

$32$

$36$

$48$

$64$

答案：E

知识点：正方形（几何）圆

难度评级：980

解答：

每个半圆建在长度为 $4$ 的边上，所以半径为 $2$ 。每个半圆从原正方形的一边向外突出一个半径。

$ABCD$ 的每条边等于原边长加两个半径： $4 + 2(2) = 8$ 。所以 $ABCD$ 的面积是 $8^2 = 64$ 。

所以正确答案是 E。

Each semicircle is built on a side of length $4,$ so its radius is $2.$ A semicircle bulges out from the middle of each side by that radius.

Each side of $ABCD$ is the original side plus two radii: $4 + 2(2) = 8.$ So the area of $ABCD$ is $8^2 = 64.$

Thus, the correct answer is E .

1994 AMC 8 第 19 题

答案：E

难度评级：980

解答：

其他年份的第 19 题