Answer
$11\pi-12\sqrt 2$
or $17.6$
Work Step by Step
$A=2.\frac{1}{2}\int_{\pi/4}^{5\pi/4}(3+2cos\theta)^{2}d \theta$
$=\int_{\pi/4}^{5\pi/4}(11+12cos\theta+2cos2\theta)d \theta$
$=[11\theta+12sin\theta+sin2\theta]_{\pi/4}^{5\pi/4}$
$=11\pi-12\sqrt 2$
or
$=17.6$
