In the diagram, K, O and M are the centers of the three semi-circles. OC = 32 and CB = 36,

Ok let's do this

the diameter of circle  M is [36] so the radius is 18, the area of semicircle M is 18^2*pi which is 324pi then /2 which is 162pi

Now let's move on, the radius of circle O=32+36 which is 68, that will equal to (68^2)/2 which is 2312 and the diameter is [136]

 

Now with these two Diameters, we can find the area of circle K, first we find the radius, that will be (136-36)/2 which is 50, then 50^2/2 which is 1250, finally multiply by pi and we get

 

 

 

                                                                                           1250pi

OB = OC + CB = 68

 

Radius AK = OB - MB = 50

 

Area of the semi-circle with center k...  A = (50²pi) / 2