Answer
$A=\frac{s^{2}}{2\theta}$
Work Step by Step
Step 1: $A=\frac{1}{2}r^{2}\theta$
Step 2: $A=\frac{1}{2}\times r\times r\times\theta$
Step 3: Since $s=r\times\theta$,
$A=\frac{1}{2}\times r\times (r\times\theta)$
Step 4: $A=\frac{1}{2}\times r\times (s)$
Step 5: $A=\frac{1}{2}\times r\times (s)$
Step 6: Rearranging $s=r\theta$ as $r=\frac{s}{\theta}$ and substituting,
$A=\frac{1}{2}\times \frac{s}{\theta}\times s$
Step 7: $A=\frac{s^{2}}{2\theta}$