Question

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

$16$

$32$

$36$

$48$

$64$

Solution:

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 Problem 19

Solution:

Problem 19 in Other Years