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

Given the figure:

The circle has a radius of 6 units. An included angle of 120 degrees. The shaded portion is outside the circle with sides tangent to the circle. 

We can draw two right triangles by drawing a line bisecting the included angle. Then, we use the Pythagorean theorem to solve for the measurement of the two sides. 

let x = measure of the side of the shaded portion

tan (60) = opposite / adjacent
tan (60) = x / 6

solve for x, x = 10.39

let s = arc

s = rθ
s = 6 * 120*pi/180
s = 4*pi

then solve for the area of the shaded portion. 

Main idea on left, details on right