AMC8 1994
AMC8 1994 · Q19
AMC8 1994 · Q19. It mainly tests Area & perimeter, Ratios in geometry.
Around the outsides of a 4 by 4 square, construct four semi-circles (as shown in the figure) 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 semicircle. The area of the square ABCD is
在一个4×4的正方形外侧，用正方形的四条边作为直径，构造四个半圆（如图所示）。另一个正方形ABCD，其边与原正方形对应边平行，ABCD的每条边与一个半圆相切。ABCD正方形的面积是
(A)
16
16
(B)
32
32
(C)
36
36
(D)
48
48
(E)
64
64
Answer
Correct choice: (E)
正确答案：（E）
Solution
Semicircle radius 2. ABCD side =4 +2×2=8, area 64.
半圆半径2。ABCD边长=4+2×2=8，面积64。
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