Square ABCD has sides of length 1. Find the area common to the circles of radius 1 with centers at A and C.
+130511 See the following image
Using symmetry the top half of the common area can be found as follows :
Area of (1/4)circle with a radius of 1 - Area of right triangle with legs of 1 =
(1/4) pi (1)^2 - (1/2)(1)^2 =
pi/4 - 1/2
So.....the total common area = 2 (pi/4 - 1/2) = pi/2 - 1 units^2
