What is the area of the marked region?



The area of the marked region plus the area of the circle with radius \(1\) equals to the area of the square with side length \(2\), because radius of the circle is \(1\) and we have cut the blue star shape in four equal parts to construct the square in the way the picture above shows.
Hence the area of the marked region is \[A + \pi = 4 \implies A = 4-\pi\,.\]