Answer
$8$
Work Step by Step
Given: $r=-1+\cos \theta$
The length is given as follows:
$L= \int_{0}^{2\pi} \sqrt{(-1+\cos \theta)^2+(-\sin \theta)^2} d\theta$
Then, $L=\int_{0}^{2\pi} (2) \sin (\dfrac{\theta}{2}) d\theta$
After solving, we get $A=-4(-1)-(-4)=8$
