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

Side of the square ABCD = AB

= 3 × diameter of circular design

\( = \ 3 \ × \ (2 \ × \ 7) \ = \ 42 \) cm

\(\therefore \) Area of the square ABCD \( = \ 42 \ × \ 42 \ = \ 1764 \) cm²

Area of one circular design \( = \ \pi r^2 \)

\( = \ \frac{22}{7} \ × \ 7 \ × \ 7 \ = \ 154 \) cm²

\(\therefore \) Area of 9 such designs \( = \ 9 \ × \ 154 \ = \ 1386 \) cm²

\(\therefore \) Area of the remaining portion of the handkerchief

= Area of the square ABCD - Area of 9 circular designs

\(= \ 1764 \ - \ 1386 \ = \ 378 \) cm²