There is no simple answer here as it really is up to you if you feed your wedding photographer or not. Some wedding photographers do request it if they are working over a certain number of hours or some wedding venues may suggest that you feed your wedding photographer. The answer though is you don’t have to feed them.
From a personal point of view, as a wedding photographer, it is nice to be asked. That said I do prefer to ‘eat on the go’. A quick sandwich at the bar is good for me. While I may not be taking many photographs while your wedding guests are all sat down eating (not sure why but people apparently don’t like photos of them with their mouths full) there are still other things that I should be doing rather than putting my feet up.
It also depends on how long your wedding photographer will be there. If they are only there to photograph the ceremony and reception, then food may not be needed. If they are going to be there all day though it may be an option that you may want to consider asking them about, it really is a personal choice depending on your photographer.
If you decide that you do want to feed your photographer then that leaves another question. Where are you going to sit them while they eat?
For the majority of wedding where I have been fed, I have been sat away from the guests, either at the bar or in another room. There have also been times where I have been invited to sit with the guests while we all enjoy the same meal together. Both of these approaches have their advantages.
When I have been sat at the bar, it is an opportunity for me to have a bit of a break and relax (it can be stressful photographing a wedding). Sitting at the table with the guests though gives me the opportunity to socialise with them so that they can be more comfortable with me around and relaxed when I decide to point the camera at them later in the evening.
It is your choice if you feed your wedding photographer, I would suggest though that you do speak to them about it though as they may have their own opinion on the subject.