AMC 8 1994 Problem 19
AMC8 1994 年第 19 题
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Around the outside of a 4 by 4 square, construct four semicircles (as shown in the figure) with the four sides of the square as their diameters. Another square, , has its sides parallel to the corresponding sides of the original square, and each side of is tangent to one of the semicircles. The area of the square is
在一个 4 × 4 正方形的四边外侧，以正方形的四条边为直径作四个半圆（如图所示）。另一个正方形 的各边与原正方形的对应边平行，且 的每条边都与一个半圆相切。正方形 的面积是
- A.16
- B.32
- C.36
- D.48
- E.64
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
The radius of each semicircle is 2, half the sidelength of the square. The line straight down the middle of square is the sum of two radii and the length of the smaller square, which is equivalent to its side length. The area of is .
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