Concept:Area of a circle is given by:A = ?r2r = radiusArea of a rectangle is given by:A = a × ba = length of the rectangleb = breadth of the rectangleFor the rectangle to have a maximum area, the two sides must be of equal length, i.e.For a = b, the area will be maximum.Application:The area of the rectangle will be maximum when both the sides are of equal length, as shown:Applying Pythagoras theorem, we can write:x2 + x2 = (2a)22x2 = 4a2\(x = \sqrt 2 a\)The maximum area of the rectangle wll be:A = x2 = 2a2Area of circle = ?a2The area of the shaded portion will be the difference between the two, i.e.Area of the circle “ Area of rectangle= ?a2 “ 2a2