Find the area of the shaded region.

Solution:

Area of the shaded region = Area of Big square - Area of 4 semi-circles - Area of small square

From the figure we have, 14 = 2 x Diameter of circle + 6

8 = 2 x Diameter of circle

Diameter of circle = 4

Radius of circle = 2.

Now, the area of the semi-circle = $\frac{{\mathrm{\pi r}}^2}{2}= \frac{22}{7}\times \frac{1}{2}\times 2^2 = 6.28$

 the area of the 4 semi-circles = 25.14

Now, the area of Small square = Side x Side       [Side of square = Diameter of circle = 4cm]

= 4 x 4 = 16 cm²

Area of the shaded region = 14 x 14 - 25.14 - 16 = 196 - 25.14 - 16 = 154.86 cm².