please find the area and perimeter
Circle segment area:
$\displaystyle r\text{:=}1;$
$\displaystyle \theta \text{:=}30*\frac{\pi }{180};$
$\displaystyle \text{segmentHyG}\text{:=}\frac{1}{2}r^2(\theta -\text{Sin}[\theta ])$ = $\displaystyle \frac{1}{2} \left(-\frac{1}{2}+\frac{\pi }{6}\right)$
Central square area:
$\displaystyle (2\text{Sin}[15{}^{\circ}])^2$ = $\displaystyle \frac{1}{2} \left(-1+\sqrt{3}\right)^2$
$\displaystyle S\text{:=}4\text{segmentHyG}+(2\text{Sin}[15{}^{\circ}])^2$ = $\displaystyle \frac{1}{3} \left(3-3 \sqrt{3}+\pi \right)$
Perimeter:
Perimeter= 4$\displaystyle \text{arcHyG}\text{:=}r \theta$ = $\displaystyle \frac{2 \pi }{3}$