Express answer in exact form. a regular hexagon with sides of 3" is inscribed in a circle. find the area of a segment formed by a side of the hexagon and the circle. (hint: remember corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)

We know that
the regular hexagon can be divided into 6 equilateral triangles

area of one equilateral triangle=s²*√3/4
for s=3 in
area of one equilateral triangle=9*√3/4 in²

area of a circle=pi*r²

in this problem the radius is equal to the side of a regular hexagon
r=3 in
area of the circle=pi*3²> 9*pi in²
we divide that area into 6 equal parts> 9*pi/6> 3*pi/2 in²

the area of a segment formed by a side of the hexagon and the circle is equal to 1/6 of the area of the circle minus the area of 1 equilateral triangle
so
 [ (3/2)*pi in²-(9/4)*√3 in²]

the answer is
 [ (3/2)*pi in²-(9/4)*√3 in²]