What's the significance of the triangular region for calculating the deadweight loss? I am familiar with the concept of deadweight loss but I can't deduce the significance of the triangular region we consider deadweight loss as.

I mean what's the issue with taking the deadweight loss as the area under ABCD instead of CDE or for that matter CDF (F being the mid point of DE) or does that particular area represents some quantity from economic perspective that I might be missing out on?
I suspect your chart could look more like this:



Initially with the price and quantity at E, the combined surplus is the triangle to the left (between the orange line and the lower green line to the left of E, i.e. the pink and grey areas).

But with for example a tax, the new equilibrium has consumers paying the price at C, so the new combined surplus is still between the orange line and the lower green line, but only to the left of C (i.e. the pink area).

So the deadweight loss is the triangle CEF (i.e. the grey area) which is the loss in surplus associated with the reduced quantity.  If all three lines are straight, and the green lines are parallel then this is the same area as the triangle CDE, but not necessarily otherwise.