A 2×3 rectangle has vertices as (0,0), (2,0), (0,3) and (2,3). It rotates 90◦ clockwise about the point (2,0). It then rotates 90◦ clockwise about the point (5,0), then 90◦ clockwise about the point (7,0), and finally, 90◦ clockwise about the point (10,0). (The side originally on the x-axis is now back on the x-axis.) Find the area of the region above the x-axis and below the curve traced out by the point whose initial position is (1,1).