Q. 74.4( 169 Votes )

In Fig. 12.25, ABCD is a square of side 14 cm. With centers A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.

Answer :

To Find: Area of shaded region

Given: Side of square ABCD = 14 cm

Radius of circles with centers A, B, C and D = 14/2 = 7 cm

Area of shaded region = Area of square - Area of four sectors subtending right angle

Area of each of the 4 sectors is equal to each other and is a sector of 90° in a circle of 7 cm radius. So, Area of four sectors will be equal to Area of one complete circle

Area of 4 sectors = Πr2

Area of square ABCD = (Side)2

Area of square ABCD = (14)2

Area of square ABCD = 196 cm2

Area of shaded portion = Area of square ABCD - 4 × Area of each sector

= 196 – 154

= 42 cm2

Therefore, the area of shaded portion is 42 cm2

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