On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Solution:

9 = Number of circular designs

7 cm = Radius of the circular design

One side of a square handkerchief has three circles.

The side of the square = 3×diameter of circle = 3×14 = 42 cm

Squares’ area = 42×42 cm2 = 1764 cm2

The circles’ area = π r= (22/7)×7×7 = 154 cm2

Designs total area = 9×154 = 1386 cm2

Area of the square – Total area of the design = Area of the remaining portion of the handkerchief =1764 – 1386 = 378 cm2