Check the picture below.
[tex]\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left[\cfrac{\pi \theta }{180}-sin(\theta ) \right]~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r = 7\\ \theta =150 \end{cases} \\\\\\ A=\cfrac{7^2}{2}\left[\cfrac{\pi (150) }{180}-sin(150^o ) \right]\implies A=\cfrac{49}{2}\left[ \cfrac{5\pi }{6}-\cfrac{1}{2} \right]\implies A = \cfrac{245\pi }{12}-\cfrac{49}{4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 51.8909~\hfill[/tex]
