In the figure (i) given below, ABCD is a square of side 14 cm and APD and BPC are semicircles. Find the area and the perimeter of the shaded region.

Area of square = (side)² = 14² = 196 cm².

From figure,

Diameter of both semicircle = side of square = 14 cm.

∴ Radius (r) = $\dfrac{14}{2}$ = 7 cm.

Area of both the semi-circles = $2 \times \dfrac{πr^2}{2}$

$= 2 \times \dfrac{\dfrac{22}{7} \times 7^2}{2} \\[1em] = 2 \times \dfrac{22 \times 49}{7 \times 2} \\[1em] = 22 \times 7 \\[1em] = 154 \text{ cm}^2.$

Area of shaded region = Area of square - Area of semi-circles

= 196 - 154 = 42 cm².

From figure,

Perimeter = arc DPA + DC + arc CPB + AB

= πr + 14 + πr + 14

= 2πr + 28

= $2 \times \dfrac{22}{7} \times 7$ + 28

= 44 + 28 = 72 cm.

Hence, area of shaded region = 42 cm² and perimeter = 72 cm.