3.14: Arc length from sector area; shaded isosceles region

The area of a sector of a circle of radius $24$ is $432\text{ cm}^{2}$. Find the length of the arc of the sector.

The diagram shows an isosceles triangle $OAB$, with $AO = AB = y$ and height $AD$. $OCD$ is a sector of the circle with centre $O$. Angle $AOB$ is $\alpha$.

Find an expression for $OB$ in terms of $y$ and $\alpha$.

Hence show that the area of the shaded region can be written as $\dfrac{y^{2}}{2}\cos\alpha\,(2\sin\alpha - \alpha\cos\alpha)$.