Question

In the figure two congruent circles touch each other externally and
touches the sides of the rectangle ABCD. If AB = 28 cm and BC - 14 cm,
find the area of the shaded region.
D​

Answer 1

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