Answer
Perimeter = 24 + 9$\pi$ in
Area = $24 \pi in^{2}$
Work Step by Step
Perimeter of sector = 2*radius + l(CD)
In a circle whose circumference is c, the length l of an arc whose degree measure is m is given by l =$\frac{m}{360}$ * c
Therefore for given circle c = 2$\pi$ r = 2$\pi$ * 12 = 24$\pi$ in
l =$\frac{135}{360}$ * 24$\pi$ in
= $\frac{3}{8}$ * 24$\pi$ in
= 9$\pi$ in
Perimeter of sector = 2* radius + l
= 2* 12 +9$\pi$ in
= 24 + 9$\pi$ in
In a circle of radius length r , the Area A of the sector whose arc has degree measure m is
A = $\frac{m}{360}$ * $\pi r^{2}$
= $\frac{60}{360}$ * $\pi 12^{2}$
= $\frac{1}{6}$ * 144$\pi $ = $24 \pi in^{2}$
Therefore the area of the sector = $24 \pi in^{2}$
