A circle has equation $x ^ { 2 } + y ^ { 2 } - 18 x - 22 y + 178 = 0$
A regular hexagon is drawn inside this circle so that the vertices of the hexagon touch the circle.
What is the area of the hexagon?
A 6
B $6 \sqrt { 3 }$
C 18
D $18 \sqrt { 3 }$
E 36
F $36 \sqrt { 3 }$
G 48
H $48 \sqrt { 3 }$