Given:
Side length = 12 in
To find:
The area of the regular polygon.
Solution:
Number of sides (n) = 6
Let us find the apothem using formula:

where s is side length and n is number of sides.




Area of the regular polygon:




in²
The area of the regular polygon is 374.1 in².
Let, coordinate of point A' is (x,y).
Since, A' is the symmetric point A(3, 2) with respect to the line 2x + y - 12 = 0.
So, slope of line containing A and A' will be perpendicular to the line 2x + y - 12 = 0 and also their center lies in the line too.
Now, their center is given by :

Also, product of slope will be -1 .( Since, they are parallel )

x = 2y - 1
So, 
Also, C satisfy given line :

Also,

Therefore, the symmetric points is
.