But what you want is this:
is a circle, centre O, radius 10.
is a straight line through through perpendicular to the initial line. (Check it out: draw this line, and join any point on it to O, and then look at the value of .)
So you need the area of the segment of the circle radius 10, cut off by a chord that is 6 units from the centre of the circle. (You get a 6, 8, 10 triangle, so it's very easy!)