Process?

let the intersection points be a.b and the points at which circles touch the rectangle be c,b. center of rect be o. no consider the sector area acb. now remove the area of triangle is abo from this. this will give 1/4 th area of the shaded part. 

total area will be 60

Say related to circles. Ellipse isnt under discussion 

find the area of the elipse with minor radius as 7/2 and major radius as 7/2*(Sqrt(3))