Let x = AD

So, AF = x/4

And, DG = x/2

Let h = altitude of the parallelogram where BC and AD are the bases.

So, x*h = 200 sq.cm

Area of any triangle = (1/2)(base)(altitude)

The triangle ABF:

base = AF = x/4

altitude = h also

So, area = (1/2)(x/4)(h) = (1/8)(hx) = (1/8)(200) = 25 sq.cm

The triangle CDG:

base = DG = x/2

altitude = h also

So, area = (1/2)(x/2)(h) = (1/4)(hx) = (1/4)(200) = 50 sq.cm

Therefore,

area of BCGF = 200 -50 -25 = 125 sq.cm -------answer.