Though less common in JEE Main, polar area problems do appear. The area enclosed by r = f(theta) from theta1 to theta2 is A = (1/2) * integral from theta1 to theta2 of [f(theta)]^2 d(theta). For a full cardioid r = a(1 + cos(theta)), the area is (1/2) * integral from 0 to 2pi of a^2(1 + cos(theta))^2 d(theta) = (3pia^2)/2. For the rose curve r = acos(2theta), each petal has area pia^2/8, and with 4 petals the total is pi*a^2/2. The key challenge is determining the correct angular limits for the desired region.