It's easy to show by the formula for the sum of the angles that
each interior angle is 120°, whose supplement is 60°.

Now we draw in some green lines to enclose the hexagon in a rectangle.
We have added four 30°-60°-90° right triangles to the hexagon.

 

In a 30°-60°-90° right triangle the shorter leg
is one-half of the hypotenuse.  And the longer leg
is the shorter leg times √3.

Since we know all 4 hypotenuses, we can find the dimensions
of the enclosing rectangle. 

 

The area of the big rectangle is 

(length)(width)= (9)(3√3) = 27√3

The area of each of the two larger 30°-60°-90° right triangles
is  

(base)(height)/2 = (2)(2√3)/2 = 2√3

The area of both of them is 4√3

The area of each of the two smaller 30°-60°-90° right triangles
is  

(base)(height)/2 = 1(√3)/2 = √3/2

The area of both of them is √3

We get the area of the hexagon by subtracting the
areas of the 4 right triangles:

27√3 - 4√3 - √3 = 22√3

Edwin