Notice that the perimeter in the figure consists of 2 sides equal to the radius of the circle and the arc that corresponds to a fraction of a whole circumference of a 14 cm radius.
[tex]\begin{gathered} P=14+14+\text{arc} \\ \text{and} \\ P=39 \\ \Rightarrow\text{arc}=39-14-14=11 \\ \Rightarrow\text{arc}=11 \end{gathered}[/tex]And,
[tex]\begin{gathered} \text{arc}=2\pi r(\frac{\theta}{2\pi}) \\ \Rightarrow\text{arc}=r\theta \\ \Rightarrow\theta=\frac{arc}{r}=\frac{11}{14} \end{gathered}[/tex]Where theta is in radians.
The area of an arc is given by the equation:
[tex]A_{\text{arc}}=r^2\pi(\frac{\theta}{2\pi})[/tex]Finally,
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