Question 1126641
The circle has center (6, -3 sqrt (3))
{{{graph(300,300,-15,15,-15,15,-3*sqrt(3)+sqrt(-(x-6)^2+36),-3*sqrt(3)-sqrt(-(x-6)^2+36))}}}

That is required for the circle to touch the y-axis.  The radius is 6 units, and the triangles made by having the center go to the x-intercepts have length 6 and the distance to the y-axis is 3 sqrt(3) by the Pythagorean theorem, given that the intersection point is (6, 0).  That makes the segment of each on the y-axis 3, and makes the two central angles 30 degrees each, since 3 is half of 6, and the sine of 30 is 1/2.

the area of the sector bounded by the  x-intercepts and the center is 1/6 of the area of the whole circle (36 pi).  The area of the part below the y-axis has length 6 and altitude 3 sqrt(3), the distance to the center from the y-axis.  That area is 3*3 sqrt (3) or 9 sqrt(3)
Therefore, the area of the segment above the y-axis is 6 pi-9 sqrt (3), which is a reasonable answer.  This is 3.26 units using approximations.