NIO and his little four-year-old sister, Yasa, were doing the paper-cutting. NIO drew several line segments and get a close area, a polygon, from a mathematical inequality, ∣x∣+∣y∣+∣x+y∣≤n. And Yasa drew a circle and its center is coincide with the polygon's center that NIO created. The radius of the circle is half of n.
They wanted to cut out union area of the polygon and the circle. Assume that they play the cutting game based on a infinite paper. What is the size of the area they cut from the paper?