I am using an LED as a point source for a school project. I have two questions in regards to the LED(s).

I know that light follows the inverse square law when measuring perceived brightness, but all sources I can find show examples of a round bulb light. Is there an altered version of the formula for LED’s that incorporates factors such as the fan angles?

Also, I will most likely be adding more LED’s to my project to increase the total lumens/lux. I’ve seen many people ask the question whether lumens will add in such a scenario. In theory they would but it wouldn’t be perceived that way. My question is; is there a formula/equation/calculation that can help me predict the lumens perceived by x number of LED’s, d inches apart from one another, measured at y feet away, with regard to joining and isolated parts of the fan angles of each LED.