In the figure (i) given below, ABCD is a rectangle, AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of the shaded portion.

Since, ABCD is a rectangle.

AD = BC = 7 cm.

CD = AB = 14 cm.

From figure,

AD and BC are diameters of smaller circles.

Radius = $\dfrac{7}{2}$ = 3.5 cm.

Area of each small semi-circle = $\dfrac{πr^2}{2}$

= $\dfrac{22}{7} \times (3.5)^2 \times \dfrac{1}{2}$

= 19.25 cm².

From figure,

CD is the diameter of the larger semi-circle.

Radius = $\dfrac{14}{2}$ = 7 cm.

Area of larger semi-circle = $\dfrac{πr^2}{2}$

= $\dfrac{22}{7} \times (7)^2 \times \dfrac{1}{2}$

= 77 cm².

Area of rectangle ABCD = AB × BC

= 14 × 7

= 98 cm².

From figure,

Area of shaded region = Area of rectangle ABCD + 2 × Area of each smaller semi-circle - Area of larger semi-circle

= 98 + (2 × 19.25) - 77

= 98 + 38.5 - 77

= 59.5 cm².

Hence, area of shaded region = 59.5 cm².