Chapter 11: Parametric Equations and Polar Coordinates - Section 11.5 - Areas and Lengths in Polar Coordinates - Exercises 11.5 - Page 671: 24

$2a$

The length of the curve can be calculated as: $L=\int_{p}^{q}\sqrt{r^2+(\dfrac{dr}{d\theta})^2}d\theta$ Here, we have $L=\int_{0}^{\pi} \sqrt{a^2(\dfrac{(1-\cos \theta)}{2})^2+(\dfrac{(a) \sin \theta}{2})^2} d \theta=(\dfrac{a}{2}) \int_{0}^{\pi} \sqrt {2 (1-\cos \theta)} d\theta$ or, $L =a [2\cos (\theta/2)]_{0}^{\pi}=2a$