Find value of \(\theta\),
\(\begin{aligned} s&=r\theta \\\\ 9&=(7)\theta \\\\ \theta&=\dfrac{9}{7}\text{ rad} .\end{aligned}\)
Convert \(\theta\) to degrees,
\(\begin{aligned} \theta&=\dfrac{9}{7}\text{ rad}\times\dfrac{180^\circ}{3.142} \\\\ &=73.66^\circ .\end{aligned}\)
Find the length of chord \(AB\),
\(\begin{aligned} AB&=2j \sin \dfrac{\theta}{2} \\\\ &=2(7) \sin \begin{pmatrix} \dfrac{73.66}{2} \end{pmatrix} \\\\ &=14 \times \sin 36.83^\circ \\\\ &=14 \times 0. \, 5994 \\\\ &= 8. \,3916 \text{ cm}. \end{aligned}\)
The perimeter of the shaded segment \(APB\),
\(\\ \ = \text{Length of Chord } AB + \text{Arc Length } APB \\\\\)
\(\begin{aligned} &=8. \,3916+9 \\\\ &=17.39 \text{ cm} .\end{aligned}\)
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