Region R consists of all points inside the square that are closer to the center of the square than to any of the sides. Find the area of R

http://img.photobucket.com/albums/v3...epinoy/box.jpg
Just to verify the length of the sides of the square is 2.

Right now i'm just focusing on quadrant I and making a triangle. Then i make the outside point of Region R say, point P, from the right side 1-x and from the top 1-y. But then i don't know where to go from there. At first i thought it was a circle but its not.