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# 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. Q.11

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In chapter areas related to circles of ncert class 10 what is the best solution of exercise 12.3 question number 11 .Find the best and easiest way to solve this question , its very tricky question of this chapter give me the simplest solution of this question.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.

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1. Number of circular designs = 9

Radius of the circular design = 7 cm

There are three circles in one side of square handkerchief.

∴ Side of the square = 3×diameter of circle = 3×14 = 42 cm

Area of the square = 42×42 cm2 = 1764 cm2

Area of the circle = π r= (22/7)×7×7 = 154 cm2

Total area of the design = 9×154 = 1386 cm2

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

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