Question 149138
You could try proportions on this problem:
Let's compare the ratio of the arc length, S, to the circumference of the circle, C, with the ratio of the area enclosed by the sector {{{A[s]}}} to the area of the entire circle {{{A[c] = (pi)r^2}}}. Remember that {{{C = 2(pi)r}}}
{{{S/C = A[s]/A[c]}}}
{{{S/2(pi)r = A[s]/(pi)r^2}}} Simplify and solve for {{{A[s]}}}
{{{S(pi)r^2/2(pi)r = A[s]}}}
{{{A[s] = Sr/2}}}