A square ABCD is inscribed in a circle of unit radius. Semicircles

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A square ABCD is inscribed in a circle of unit radius. Semicircles are described on each side as a diameter. The area of the region bounded by the four semicircles and the circle is

1. 1 sq. unit
2. 2 sq. unit
3. 1.5 sq. unit
4. 2.5 sq. unit

Correct Option: B

As per the given in question , we draw a figure square ABCD in which is inscribed in a circle of unit radius ,

BD = 2 units
AB = √2 units
Area of square = 2 square units

Area of four semicircles = 4 ×	πr²
	2

Area of four semicircles =	4 × π × 1/2
	2

Area of four semicircles = πsq. units
∴ Required area = 2 + π – π = 2 sq. units.