2021 April MIMC 10 Problems/Problem 23
On a coordinate plane, point denotes the origin which is the center of the diamond shape in the middle of the figure. Point has coordinate , and point , , and are formed through , , and rotation about the origin , respectively. Quarter circle (formed by the arc and line segments and ) has area . Furthermore, another quarter circle formed by arc and line segments , is formed through a reflection of sector across the line . The small diamond centered at is a square, and the area of the little square is . Let denote the area of the shaded region, and denote the sum of the area of the regions (formed by side , arc , and side ), (formed by side , arc , and side ) and sectors and . Find in the simplest radical form.
To be Released on April 26th.