PQRS is a diameter of a …

PS = Diameter of a circle of radius 6 cm = 12 cm
{tex}\therefore{/tex} PQ = QR = RS = {tex}\frac { 12 } { 3 }{/tex}= 4cm, QS = QR + RS = (4 + 4)cm = 8 cm
Let P be the perimeter and A be the area of the shaded region.
P = Arc of semi-circle of radius 6 cm + Arc of semi-circle of radius 4 cm + Arc of semi-circle of radius 2 cm

{tex}\Rightarrow P = ( \pi \times 6 + \pi \times 4 + \pi \times 2 ) \mathrm { cm } = 12 \pi \mathrm { cm }{/tex}
and, A = Area of semi-circle with PS as diameter + Area of semi-circle with PQ as diameter - Area of semi-circle with QS as diameter.
{tex}\Rightarrow A = \frac { 1 } { 2 } \times \frac { 22 } { 7 } \times ( 6 ) ^ { 2 } + \frac { 1 } { 2 } \times \frac { 22 } { 7 } \times 2 ^ { 2 } - \frac { 1 } { 2 } \times \frac { 22 } { 7 } \times ( 4 ) ^ { 2 }{/tex}
{tex}\Rightarrow A = \frac { 1 } { 2 } \times \frac { 22 } { 7 } \left( 6 ^ { 2 } + 2 ^ { 2 } - 4 ^ { 2 } \right) = \frac { 1 } { 2 } \times \frac { 22 } { 7 } \times 24 = \frac { 264 } { 7 } \mathrm { cm } ^ { 2 }{/tex} = 37.71 cm²