Data:
r= 3.5cm
α= 5π/6
To find the area of a sector in a circle you can use the next formula:
[tex]A_s=\pi\cdot r^2\cdot\frac{\alpha}{2\cdot\pi}[/tex]Then, the area of the given sector is: 16 square centimeters[tex]\begin{gathered} A=\pi\cdot(3.5\operatorname{cm})^2\cdot\frac{\frac{5\pi}{6}}{2\cdot\pi} \\ \\ A=12.25\pi\cdot cm^2\cdot\frac{5\cdot\pi}{12\cdot\pi} \\ \\ A=\frac{61.25\pi cm^2}{12}\approx16.0\operatorname{cm}^2 \end{gathered}[/tex]