The area of the shaded region in figure, if ABCD is a square of side 7cm and APD and BPC are semicircles is

Side of the square ABCD = diameter of the semicircle = 7 cm

    $\therefore Radius=\frac{7}{2}cm$

 Area of square $=S\times S=7\times 7=49c{m}^2$

  Area of semicircle APD = Area of semicircle BPC $=\frac{1}{2}\pi r^2$

  $=\frac{1}{2}\times \frac{22}{4}\times \frac{7}{2}\times \frac{7}{2}=\frac{77}{4}c{m}^2$

  Area shaded region $=\left(\text{Area of square }ABCD\right)-2\left(\text{Area of semicircle}\right)$

   $S^2-2\left(\frac{1}{2}\pi r^2\right)=49-(2\times \frac{1}{2}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2})$

  $=49-\frac{77}{2}=\frac{98-77}{2}=\frac{21}{2}=10.5c{m}^2$