two circles both of raddi 1 intersect such that the circumference of each passes through the centre of each other find the area of intersecting region

Join both the points of intersection to the center of one of the circles and join the two points of intersection with each other. In this triangle, two of the sides are 1 each (radii) and the included angle is 120 degrees. The required area = 2*(area of the sector with angle 120 - area of the triangle) = 2*($$\pi/3 - 1/2*1*1*\sqrt3/2$$) = 2*$$(\pi/3 - \sqrt3/4)$$