Given:
#r=a(1-cosθ)#
#intrd(theta)=inta(1-costheta)d(theta)#
between #theta=0# to #theta=2pi#
#|(0 and pi/2)|#, #|(pi/2# and #pi)|#, #|(pi and (3pi)/2)|#, #|((3pi)/2,2pi)|#
#=|a(theta-sintheta)|#
#=|a(pi/2-sin(pi/2))-a(0-sin0)|#
#+|a(pi-sinpi)-a(pi/2-sin(pi/2))|#
#+|a((3pi)/2-sin(pi)/2)-a(pi-sinpi)|#
#+|a(2pi-sin2pi)-a((3pi)/2-sin((3pi)/2))|#
#=|a(pi/2-1)-a(0-0)|#
#+|a(pi-0)-a(pi/2-1)|#
#+|a((3pi)/2-(-1))-a(pi-0)|#
#+|a(2pi-0)-a((3pi)/2-(-1))|#
#a{(pi/2-0)+(pi-pi/2+1)+((3pi)/2+1-pi)+(2pi-(3pi)/2+1)}#
#a{pi/2+pi/2+1+(5pi)/2+1+pi/2+1}#
Area enclosed by the curve, #r=a(1-cosθ)#is
#A=a{2pi+3}#
