Question 75245
Formula for a segment of a circle is {{{a = (1/2)*((r*L)-c(r-h))}}}

given: r =12, c = 20

First, we must find "h" & "L"

To find "h":
{{{h = r-(1/2)*sqrt(((4)*r^2)-c^2)}}}
{{{h = 12-(1/2)*sqrt((4*12^2)-(20^2))}}}
{{{h = 12-(1/2)*sqrt(576-400)}}}
{{{h = 12-(1/2)*sqrt(176)}}}
{{{h = 12-(1/2)*(13.26649916)}}}
{{{h = 12-(6.633249581)}}}
{{{h = 5.366750419}}}

Next, find "L":
{{{L = 0.01745*r*angle}}}

we dont know the angle yet, so solve for the angle first:
{{{SinX = (10/12)}}}
{{{SinX = .833333333}}}
{{{Sin^-1(.833333333) = X}}}
{{{56.44269024 = X}}}
multiply by 2 to get total angle;
{{{56.44269024*2 = 112.8853805}}}

now solve for "L":
{{{L = 0.01745*r*angle}}}
{{{L = 0.01745*12*112.8853805}}}
{{{L = 23.63819867}}}

Now solve for area:
{{{a = (1/2)*((r*L)-c(r-h))}}}
{{{a = (1/2)*((12*23.63819867)-20(12-5.366750419))}}}
{{{a = (1/2)*((283.658384)-20(6.633249581))}}}
{{{a = (1/2)*((283.658384)-(132.6649916))}}}
{{{a = (1/2)*(150.9933924)}}}
{{{a = 75.4966962}}}
so the approximate area is {{{75.5m}}}