Filling areas using transparent color without affecting the border, in Illustrator CS6

In Illustrator, if you want to fill in areas surrounded by multiple line segments, you can first select all the line segments and use Live Paint Bucket (K) to fill the color. However, if you want to change the opacity of the area, you may find the borders also become transparent, like this:

My question is, is there any way to avoid the border changing its transparency when we change the transparency of its internal area?

Note: there are 3 line segments, with endpoints connected. An extended question, what if one of the line is dashed? This question originally comes from the fact that I want to fill the triangles as the bottom figure shows.