Circumference of a circle is 132 cm. What is the perimeter of its sector whose central angle is $$135^\circ$$ ?

Circumference of a circle, $$ 2 \times \frac{22}{7} \times R = 132cm $$

solving, R=21 cm

Here central angle of sector = $$ 135^\circ $$

Length of arc = $$ (\frac{\theta}{360}) \times 2 \times \frac{22}{7} \times R $$

                     = $$ \frac{135}{360} \times 2 \times \frac{22}{7} \times 21 $$

                     =49.5 cm

 perimeter of sector =$$ Length of arc + 2 \times R $$

                               =$$ 49.5 + 2 \times 21 $$

                               = 49.5 + 42

                               = 91.5 cm