Question 34342
First find out how much of the whole circle is {{{(pi)/4}}}radians.
There are {{{2(pi)}}}radians in a complete circle, so you need to divide{{{(pi)/4}}} by{{{2(pi)}}}
{{{((pi)/4)/(2(pi)) = (1/8)}}}
The segment is {{{1/8}}} of the entire cicle, so the area of the segment will be {{{1/8}}} the area of the entire circle.

{{{A = (pi)r^2}}} But{{{r = d/2}}} = {{{12/2 = 6}}}
{{{A = (pi)(6^2)}}}
{{{A = (pi)36}}} This is the area of the entire circle. Divide by 8 the get the area of the segment.
{{{A/8 = 36(pi)/8}}}
{{{A/8 = (9/2)(pi)}}}

Area of the segment is:
{{{A(s) = (9/2)(pi)}}} Square inches.