$\int_0^{2\pi}\frac{1}{2}r^2d\theta$

$r^2=36+36\cos(5\theta)+9\cos^2(5\theta)$

$r^2=36+36\cos(5\theta)+9\frac{1+\cos(10\theta)}{2}$

$\int_0^{2\pi}\Big(18+18\cos(5\theta)+\frac{9}{4}+\frac{9\cos(10\theta)}{4}\Big)d\theta$

Integrate.