Question

Find the area of the shaded region.

80°
5 cm
A≈ [?] cm²
Enter a decimal rounded to the nearest tenth.

Answer 1

`\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 = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=5\\ \theta =80 \end{cases} \\\\\\ A=\cfrac{5^2}{2}\left( ~~ \cfrac{\pi (80) }{180}-\sin(80^o ) ~~ \right)\implies A=\cfrac{25}{2}\left(\cfrac{4\pi }{9}- \sin(80^o) \right) \\\\\\ A=\cfrac{50\pi }{9}-\cfrac{25\sin(80^o)}{2}\implies A\approx 5.1~cm^2`