Solution
= Solution
The <arc length> follows from the <speed> of the parametrization:
$$
\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}
=a\sqrt{2-2\cos t}=2a|\sin(t/2)|.
$$
Here $\sin(t/2)>0$ inside the given interval. Therefore
$$
\boxed{L=2a\int_0^{2\pi}\sin(t/2)dt=8a.}
$$
The result scales as a length, while the preceding area scales as $a^2$, as required by <dimensional analysis>.