Geometric interpretation of additive variance

My intuitive understanding of additive variance:
   Total variance = Var(X) + Var(Y)
  where Var(X) = sum of (x_i - mean)^2 .

So, Var(X) and Var(Y) are made of the square areas around their mean.  Total variance is the total area. Additive indicate X and Y are independent.

Co-variance will be the rectangles from this view.
Var(x+y) = Var(x) + Var(y) + 2Cor(X,Y)

I need to add a diagram to illustate this.