Question

Find the area of the shaded portion.

A=

Answer 1

shaded area = quad area - area of circle/3

Answer 2

Draw a line bisecting the 120 degree angle such that it forms 2 right triangles.
half of 120 is 60
So each right triangle is a special 30-60-90 right triangle with sides 6,6sqrt3,12
The area of each of these triangles is (6*6sqrt3)/2 thus area of both is 36sqrt3.
Then subtract area of sector which is one-third of circle
(pi*6^2)/3
A = 36sqrt3 - 12pi