Math Prize 2014 Problem 1
Source:
September 28, 2014
geometry
Problem Statement
The four congruent circles below touch one another and each has radius 1.
[asy]
unitsize(30);
fill(box((-1,-1), (1, 1)), gray);
filldraw(circle((1, 1), 1), white);
filldraw(circle((1, -1), 1), white);
filldraw(circle((-1, 1), 1), white);
filldraw(circle((-1, -1), 1), white);
[/asy]
What is the area of the shaded region?