Find the area and the perimeter of the shaded region in figure (i) given below. The dimensions are in centimeters.

From figure,

Radius of larger semi-circle (R) = 14 cm.

Area of larger semi-circle = $\dfrac{πR^2}{2} = \dfrac{22}{7} \times (14)^2 \times \dfrac{1}{2}$

$= \dfrac{22}{7} \times 196 \times \dfrac{1}{2}$

= 22 × 14

= 308 cm².

Diameter of smaller semi-circle = 14 cm; radius (r) = $\dfrac{14}{2}$ = 7 cm.

Area of smaller semi-circle = $\dfrac{πr^2}{2} = \dfrac{22}{7} \times (7)^2 \times \dfrac{1}{2}$

$= \dfrac{22}{7} \times 49 \times \dfrac{1}{2}$

= 11 × 7

= 77 cm².

From figure,

Area of shaded region = Area of larger semi-circle - Area of smaller semi-circle

= 308 - 77

= 231 cm².

From figure,

Perimeter of shaded region = Circumference of larger semi-circle + Circumference of smaller circle + 14

= πR + πr + 14

= $\dfrac{22}{7} \times 14 + \dfrac{22}{7} \times 7 + 14$

= 44 + 22 + 14

= 80 cm.

Hence, area of shaded region = 231 cm² and perimeter = 80 cm.