Circular measure — practice question

The diagram illustrates a sector of a circle, with centre $O$, for which $OB = OC = 15\text{ cm}$. The angle $BOC$ measures $\frac{2}{5}\pi$ radians. On the lines $OB$ and $OC$, points $A$ and $D$ are joined by an arc $AD$ belonging to a circle centred at $O$. The shaded part is enclosed by arcs $AD$ and $BC$ together with the straight segments $AB$ and $DC$. The area of the shaded region is given as $\frac{19}{5}\pi\text{ cm}^2$.