Answer:
69.66 cm
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.3 cm}\underline{Circumference of a circle}\\\\ $C=\pi d$\\\\where $d$ is the diameter\end{minipage}}[/tex]
From inspection of the given diagram:
- Diameter of the larger circle = 5 + 14 + 4 = 24 cm
- Diameter of the smaller circle = 14 cm
The perimeter of a two-dimensional shape is the distance all the way around the outside.
Therefore, the perimeter of the given shaded region is the sum of half the circumference of the larger circle, half the circumference of the smaller circle, and the two 5 cm ends.
[tex]\begin{aligned}\sf \implies Perimeter & = \sf \dfrac{1}{2} \pi (24) + \dfrac{1}{2} \pi (14) + 5 + 5\\& = \sf \dfrac{1}{2}(3.14)(24) + \dfrac{1}{2}(3.14)(14) +10\\& =\sf 37.68+ 21.98+10\\& =\sf 69.66\:\:cm\end{aligned}[/tex]
Therefore, the perimeter is 69.66 cm.
