ABCD is a square with sides of 1 unit. AC and BD are arcs of circles with their centers at B and A, respectively. The area of the shaded sector AED is

Given :- ABCD is a square with sides of 1 unit. AC and BD are arcs of circles with their centers at B and A, respectively.

Concept used :- To find shaded area we subtract the empty area from area of unit cube.

Solution :- Since \(\triangle ABE\) is equilateral triangle.

So area of sector AEB would be \(\pi/6\)

and area DBCD = area of square - \(\dfrac{1}{4}\)area of circle

hence area of DBCD = 1- \(\pi/4\)

So shaded area = area of square - area of DBCD - area of sector AEB

Hence shaded area = \(1-1+\pi/4-\pi/6=\pi/12\)