Question

I need help to find the area of the shaded region?

Answer 1

$\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( \cfrac{\pi \theta }{180}-sin(\theta ) \right)~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=18.6\\ \theta =123 \end{cases} \\\\\\ A=\cfrac{18.6^2}{2}\left( \cfrac{\pi (123) }{180}-sin(123^o ) \right)\implies A\approx\cfrac{345.96}{2}\left( \cfrac{41\pi }{60}-0.8386705679 \right) \\\\\\ A\approx 172.98(1.308084412)\implies A\approx 226.27244158776$