In the figure (i) given below, ABCD is a square of side 14 cm. A, B, C and D are centres of the equal circles which touch externally in pairs. Find the area of the shaded region.

Let r cm be the radius of each circle.

From figure,

⇒ r + r = AD

⇒ 2r = 14

⇒ r = 7 cm.

Hence, radius of each circle = 7 cm.

Area of each circle = πr²

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

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

= 22 x 7

= 154 cm².

Area of 4 circles = 4 × 154 = 616 cm².

From figure,

Radius of each quadrant in square ABCD = 7 cm.

Area of each quadrant = $\dfrac{1}{4}πr^2$

= $\dfrac{1}{4} \times \dfrac{22}{7} \times 7^2$

= 38.5 cm².

Area of 4 quadrants = 4 × 38.5 = 154 cm².

Area of square = (side)²

= (14)² = 196 cm².

Area of shaded region = (Area of 4 circles - Area of 4 quadrants) + (Area of square - Area of 4 quadrants)

= (616 - 154) + (196 - 154)

= 462 + 42

= 504 cm².

Hence, area of shaded region = 504 cm².