The width is no problem.....it is just 4 times the radius of each circle = 4r = 4(2mm) = 8mm (1)
Note that joining the 3 radii will form an equilateral triangle with sides = 2r = 2 * 2mm = 4mm
The height of this triangle, h, can be found as
tan 60 = h/2
sqrt (3) = h / 2
2sqrt(3) = h
So....the height of the rectangle = [ 2sqrt(3) + 2r ] mm = [ 2sqt(3) + 2(2)] mm = [ 2qrt(3) + 4 ] mm (2)
So....the area of the rectangle = (1) * (2) =
[ 8 ] * [ 2sqrt (3) + 4 ] mm^2 =
[ 16sqrt (3) + 32 ] mm ^2