+109 The shaded region below has area a+b\pi where a and b are positive integers. What is a+b? (You may assume the boundary of each region is made up of straight lines and circular arcs, and the squares of the grid have side length $1.$)
+130555 
E = (10, 10sqrt 3) F = (10sqrt 3, 10)
The area is compsed of a square whose area = EF^2 = [ 2(10 - 10sqrt3)]^2 = 400 (2 -sqrt 3) =
800 - 400sqrt 3
And 4 equal sectors = 4 [ pi /6 * 20^2 - (1/2) (20^2) sqrt (3) /2)] = 4 (200pi/3 - 100) =
(800/3)pi - 400
Total area = 400 - 400sqrt 3 + (800/3)pi = 400 [ 1 - sqrt 3 + 2 pi / 3 ]
