CBSE Class 10 Answered

The required area is shaded = Area of hexagon - 2xArea of sector of circle close to the shaded area.

BOA = 120         .... internal angle of hexagon.

The diagonal distance in a hexagon of side X is 2X, and since the radius of the circle is the side of the hexagon,

OO' = 12 cm, and the circles touch each other.

Area of hexagon = 6xArea of an equilateral triangle with side 6 cm

= (33/2)(6x6) = 543 sq cm. = 93.53 sq cm

Area of sector = (1/2)R²θ = (6x6x2x22)/(3x2x7) = 37.68 sq cm.       .........angle subtended is 120.

Shaded area = 93.53 - 2x37.68 = 18.17 sq cm.

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