Area of the segment = (Area of sector $O A B)-($ Area of $\triangle O A B$ ) $$=\left(\frac{\pi r^{2} \theta}{360^{\circ}}-\frac{1}{2} r^{2} \sin \theta\right)=r^{2}\left(\frac{\pi \theta}{360^{\circ}}-\frac{1}{2} \sin \theta\right) .$$
Explanation as extracted from the printed page; notation may be imperfect.