Question 1142081
The nonagon has nine of these isosceles triangles:
Peak angle 40 degrees
Each base angle 70 degrees
Let r be distance peak to base angle
Let a be altitude of one isosceles triangle


{{{r/sin(70)=6/sin(40)}}}

{{{r=6(sin(70)/sin(40))}}}

-

{{{a/sin(70)=r/sin(90)}}}

{{{a=r*sin(70)/1}}}

{{{a=6(sin(70)/sin(40))sin(70)}}}

{{{highlight_green(a=6*sin^2(70)/sin(40))}}}

-

Total area of nonagon

{{{highlight_green(9(1/2)*6*a)}}}

{{{9*18*sin^2(70)/sin(40)}}}

{{{(0.88302/0.64278)*9*8}}}

{{{highlight(highlight_green(222.55))}}}




----------------------------BELOW STILL WRONG-------------------------------
It has nine of these isosceles triangles:
Peak angle, 40 degrees
Each base angle, <s>25</s> degrees--------MISTAKE(Really should be {{{(180-40)/2=70}}})
Base length, 6 cm
Each congruent side, r, distance from a peak angle to base angle
-
{{{sin(40)/6=sin(70)/r}}}

{{{r/sin(70)=6/sin(40)}}}

{{{r=6(sin(70)/sin(40))}}}

The original figure is made of 18 of these right triangles:
leg r
leg {{{6/2=3}}}
-
AREA of original figure, {{{18*3*r}}}
OR
{{{18*3*6(sine(70)/sin(40))}}}