In the given figure, ABCD is a square of side 14 cm and A, B, C, D are centres of circular arcs, each of radius 7 cm. Find the area of shaded region.

Given,

ABCD is a square.

Side = 14 cm

Arcs are drawn from A, B, C, D as centres.

Radius of each arc = 7 cm

Thus, each arc is a quarter circle of radius 7 cm.

Area of square = (side)²

= 14² = 196 cm².

Area of four quarter circles:

$\text{Area of one quarter circle} = \dfrac{1}{4}πr^2 \\[1em] = \dfrac{1}{4} \times π \times 7^2 \\[1em] = \dfrac{49π}{4} \text{ cm}^2.$

For 4 quarter circles, area = 4 × $\dfrac{49π}{4}$

= 49 × $\dfrac{22}{7}$

= 22 × 7 = 154

So, Area of four quarter circles = 154 cm².

Area of shaded region = Area of square - Area of four quarter circles

Area of shaded region = 196 - 154 = 42 cm².

Hence, area of shaded region = 42 cm².