A semi-circle of diameter 1 unit sits at the top of a semi-circle of diameter 2 units. The shaded region inside the smaller semi-circle but outside the larger semi-circle is called a lune. The area of the lune is.

Step-by-step solution

area of sector O A C B= r² 2 = 1 2 3 = 6 area of shaded region = 6 - area of O A B = 6 - 3 4 Hence area of line = Area of semi-circle - area of shaded region array l = 1 2 ( 1 2 )²- ( 6 - 3 4 ) = 3 4 + 8 - 6 = 3 4 - 24 array