Slick2d - Lights with line of sight

Hello ! I am new to game developping and I am trying to find an answer and I just can’t seem to find what i need.

First of all, the idea is to have blocks block light and vision in a topdown 2D environment.
But what i do not understand is how it works. Lets say i have a point that emits light, and i have some rectangle blocks that block it, i know how to get the areas that are lit and store them as triangles, but once i have them, how do i actually light up the area?

I am using slick2D and what i initially wanted to do was to draw everything transparent with alpha at 0, and then “boost” the alpha in the triangles, but i do not understand how to do that right now. It feels like i am missing something simple and yet i cannot find it.

Is there a smarter way to go about it?

Please help !