Given, Each shaded triangle is similar to △ABC, and the shaded triangles are congruent to one another.
Let's say, h= height of △ABC and b = base of △ABC, further perpendicular at AB from point D is F and point E is H.
Given, △ABC ~ △DFG, So, AC/CB = DF/FG or, h/b = DF/FG
Now, △ABC ~ △ADF. (A-A-A rule)
So, AB/AC = AD/DF or, [Sqrt (h^2 +b^2)]/h = (h/2)/DF
Similarly, △ABC ~ △EHB
So, AB/AC = EB/EH or, [Sqrt (h^2 +b^2)]/h = (b/2)/EH, So, (h/2)/DF= (b/2)/EH.
since △DFG congruent to △EGH. So, DF= EH
now, h = b and DF = h/(2*sqrt2)
So, (area of △DFG + area of △EGH) / area of △ABC = [1/2*(DF*FG)* 2] / [1/2*(AC*BC)] = 1/4.
I think B.