Given:

Side of the square = 4 cm

Radius of the quadrants at the corners = 1 cm

Radius of the circle in the centre = 1 cm

∵ 4 quadrants = 1 circle

∴ There are 2 circles of radius 1 cm

Area of square = side × side

= 4 × 4 = 16 cm²

Area of 2 circles = 2 × πr²

= 2 × × 1 × 1 = cm²

∵ Area of shaded region = Area of square – Area of 2 circles

= 16 -

= = cm² = 9.7 cm²

Hence, the area of shaded region is 9.72 cm².