Mosaic Squares

Clearly, the area of the square is $A_{\text{square}} = 4^2 = 16$ Observe that half of each square side resembles the radius of the circle, which is $2$ . Since there are $4$ semicircles, the area of all semicircles is $A_{\text{circles}} = 4 \cdot \dfrac{\pi}{2} (2)^2 = 8\pi$ Thus, $\begin{array}{rl} A_{\text{total}} &= A_{\text{circles}} + A_{\text{square}}\\ &= 8\pi + 16 \end{array}$