Cardioid

Problem
Find the area individually enclosed by the following Cardioids:
(A)   $r = a(1 - \cos \theta)$
(B)   $r = a(1 + \cos \theta)$
(C)   $r = a(1 - \sin \theta)$
(D)   $r = a(1 + \sin \theta)$
 

Problem
What is the perimeter of the curve r = 4(1 + sin θ)?
 

The answer is 32 units. For detailed solution, follow the link by clicking on the figure.
 

Example 3
Find the area inside the cardioid r = a(1 + cos θ) but outside the circle r = a.