Question 793226
Here is your pentagon (in red), with the circle, and the radii to the pentagon vertices (in green).
{{{drawing(300,300,-1.2,1.2,-1.2,1.2,
circle(0,0,1),red(line(1,0,0.309,0.951)),
red(line(0.309,0.951,-0.809,0.588)),red(line(-0.809,0.588,-0.809,-0.588)),
red(line(-0.809,-0.588,0.309,-0.951)),red(line(1,0,0.309,-0.951)),
green(line(0,0,1,0)),green(line(-0.809,0.588,0,0)),
green(line(-0.809,-0.588,0,0)),green(line(0,0,0.309,-0.951)),
green(line(0,0,0.309,0.951)),locate(0.03,0.19,72^o),
arc(0,0,0.55,-0.55,0,72)
)}}} Those radii split the pentagon into 5 congruent isosceles triangles.
The area of a triangle can be calculated as {{{a*b*sin(C)}}} if you know the measures of sides {{{a}}} and {{{b}}} and angle {{{C}}} between those two sides.
In this case, two of the sides are the radii, measuring {{{9in}}}, and the angle between them measures {{{72^o}}}.
The area of one of those triangles is
{{{(9in)*(9in)*sin(72^o)}}}= approx. {{{81*0.951}}}{{{in^2}}}={{{77in^2}}}
The area of the pentagon is approximately {{{5*77in^2=385in^2}}}