The exterior angles of a regular <em>n</em>-gon add up to 360º; here <em>n</em> = 9, so each exterior angle has measure (360/9)º = 40º.
Corresponding interior angles are supplementary to exterior angles (they add to 180º), so each interior angle has measure (180 - 40)º = 140º.
Bisect this angle by connecting any given vertex to the center of the nonagon. These connections split up the nonagon into 9 congruent isosceles triangles, each of which have base angles of 70º.
Split each triangle in half to make a total of 18 70º-20º-90º triangles with height <em>h</em> and base <em>b</em>. Then
sin70º = <em>h</em>/7 ==> <em>h</em> = 6.578
sin20º = <em>b</em>/7 ==> <em>b</em> = 2.394
and each right triangle has an area of approximately 1/2 <em>b</em> <em>h</em> = 7.874.
Multiply this by 18 to get the area of the nonagon: 141.7.
