Find the area of the shaded portion. show all work for full credit.

So.. if you notice, the central angle to that shaded section, is 120°, thus, by the "tangent segment" theorem, those two tangents are the same length, if we run an angle bisector from 120, splitting it in two 60 and 60 angles, we'll cut the angle outside the circle where the tangents meet in half

notice the picture below, you end up with two 30-60-90 triangles, to get the sides, you can use the 30-60-90 rule, in the picture, in which case, notice, x = 6

the shaded area is, the whole area of those two triangles, minus the circle's sector with the 120° angle

so.. just get the area of each triangle, 1/2 bh, add them up, THEN get the area of the circle's sector, and subtract it from the angle's sum

what you're left with, is the shaded area, the part that remains from the triangle's sum, that wasn't subtracted

and surely you know