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# 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