To calculate the area of the circle, we must calculate the radius #r# of the circle
Let the center of the circle be #O=(a,b)#
Then,
#(6-a)^2+(4-b)^2=r^2#.......#(1)#
#(6-a)^2+(5-b)^2=r^2#..........#(2)#
#(3-a)^2+(3-b)^2=r^2#.........#(3)#
We have #3# equations with #3# unknowns
From #(1)# and #(3)#, we get
#36-12a+a^2+16-8b+b^2=9-6a+a^2+9-6b+b^2#
#6a+2b=52-18=34#
#3a+b=17#.............#(4)#
From #(2)# and #(3)#, we get
#36-12a+a^2+25-10b+b^2=9-6a+a^2+9-6b+b^2#
#6a+4b=43#
#6a+4b=43#..............#(5)#
From equations #(4)# and #(5)#, we get
#34-2b=43-4b#, #=>#, #2b=9#, #b=9/2#
#3a=17-b=17-9/2=25/2#, #=>#, #a=25/6#
The center of the circle is #=(25/6,9/5)#
#r^2=(3-25/6)^2+(3-9/2)^2=(-7/6)^2+(-3/2)^2#
#=49/36+9/4#
#=130/36=65/18#
The area of the circle is
#A=pi*r^2=pi*65/18=11.34u^2#