Question 1077071
The center and any two neighboring vertices of the polygon form an isosceles triangle, base side  of length {{{1/2}}} inch.  Apex angle measure {{{360/16=22&1/2}}} degrees; each base angle  {{{78&3/4}}} degree each.


Length h, of either of the equal sides of one of these triangles:
{{{sin(22.5)/(1/2)=sin(78.75)/h}}}


{{{h/sin(78.75)=(1/2)/sin(22.5)}}}


{{{h=sin(78.75)/(2sin(22.5))}}}



The ALTITUDE of one of these isosceles triangles:
a, the altitude
{{{a^2+((1/2)/2)^2=h^2}}}


{{{a^2+(1/4)^2=(sin(78.75)/(2sin(22.5)))^2}}}


{{{a^2=(sin(78.75)/(2sin(22.5)))^2-1/16}}}


{{{a=sqrt((1/4)(sin(78.75)/sin(22.5))^2-1/16)}}}--------the altitude.
NOT finished.
Simplify this and then calculate the area for the whole polygon of 16 sides.



Area,  {{{16(1/2)(1/2)*a}}}-----substitute for a, and simplify this expression.