2006 AMC 10B Problems/Problem 6
A region is bounded by semicircular arcs constructed on the side of a square whose sides measure , as shown. What is the perimeter of this region?
Since the side of the square is the diameter of the semicircle, the radius of the semicircle is
Since the length of one of the semicircular arcs is half the circumference of the corresponding circle, the length of one arc is
Since the desired perimeter is made up of four of these arcs, the perimeter is