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.

Explanation

Given, radius of each, r = 7 cm
`:.` Diameter of circle, d= 14 cm
In a given figure, horizontal three circles touch each other
`:.` Length of square `= 3xx 14 cm = 42 cm`
Now, area of one circle `= pi r^(2) = pi (7)^(2) = (22)/(7) xx (7)^(2) = 154 cm^(2)`
`:.` Area of nine circle `= 9 xx 154 = 1386`
Now, area of square ABCD = `("side")^(2)`
`= (42)^(2) = 1764 cm^(2)`
`:.` Area of the remaining portion of the handkerchief
`:.` Area of the remaining portion of the handkerchief
= Area of square `-` Area of nine circles
`= 1764 - 1386 = 378 cm^(2)`