Draw a line from the center to each vertex:




We will calculate the area of the isosceles triangle I have made red 
at the bottom of the polygon, then multiply that area by 11.




The vertex angle of that triangle is  or ° 

To find the base angles we subtract from 180° and divide by 2:

180° -  =  = 

and half of that is , the measure of each of the base
angles of the red isosceles triangle.

Now we will draw an altitude which will cut the isosceles triangle into 
two congruent right triangles, which also divides the base into two 
2cm parts:


 
[Incidentally the length of that green line is also called the "apothem"
of the 11-gon.]

Using the right triangle on the left,

tan() = 

Solve that and get

h = 2·tan() = 7.234047843 cm  

So the area of the isosceles triangle is

A = ·base·height

A = ·4cm·7.234047843cm

A = 14.46809569 cm²

So the area of the regular 11-gon is 

11·14.46809569 cm² = 159.1490525 cm²

Edwin