[tex]L=\frac{19}{2}\pi\approx29.85in[/tex]
1) Notice that there are three semi-circles, so we have to use the formula of the Perimeter of the Circumference:
[tex]s=\frac{2\pi\text{ r}}{2}=\pi r[/tex]
2) Notice that we have in the picture, the Diameter as 8" for two semicircles and 3" for the one in the middle. So we can write out the following expression:
[tex]\begin{gathered} L=\pi r+\pi r+\pi r \\ L=4\pi+4\pi+\frac{3}{2}\pi \\ L=\frac{19}{2}\pi \end{gathered}[/tex]
Note the radius is half the diameter.
3) Hence, the length of the is 19π/2 (approximately 29.85 inches)
