On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig.). Find the area of the remaining portion of the handkerchief.

Here, we observe that,

The handkerchief is of square shape

we know that, Area of circle = ${\mathrm{\pi r}}^2$

Area of square = (side)²

Radius of each circular design, r = 7 cm

Area of the remaining portion of handkerchief = Area of the square $-$ 9 $\times$ (Area of each circular design)

Hence, Diameter = 2r = 14 cm

Thus, we get

Side of the square = 3 $\times$ diameter

= 3 $\times$ 14

= 42 cm

Area of the remaining portion of the handkerchief =Area of the square  $-$ 9 $\times$ (Area of each circular design)

= (side)² - 9${\mathrm{\pi r}}^2$

= (42)² - 9 $\times$ 22/7 $\times$ (7)²

= 1764  - 1386 

= 378 cm²