The length of the arc (s), the central angle θ, and the radius (r) are related as follows:
[tex]s=r\cdot\theta[/tex]
where θ must be in radians
The central angle related to arc length in red is 360°- 144° = 216°
360° are equivalent to 2π radians, then
[tex]\theta=216\text{ \degree}\cdot\frac{2\pi\text{ radians}}{360\text{ \degree}}=\frac{6}{5}\pi\text{ radians}[/tex]
Substituting this value of θ and r = 4 ft, the arc length is:
[tex]\begin{gathered} s=4\cdot\frac{6}{5}\pi \\ s=\frac{24}{5}\pi\text{ ft} \end{gathered}[/tex]
