Normally you will want to get a picture of the betta flaring, to show the tail fin to see what type of tail they are.
I believe you may have a halfmoon or a delta.. can't tell without seeing him flare.
As for the plakat- if he is then he is of lesser genes, as they tend to have rounder, shorter dorsal fins, and anal fins are more pointed (excluding CTPK, where the overall shape is a bit rounded). A lot of times their fins won't start to really grow until they are in a decent size tank alone- their fins tend to continue growing until around 7 months of age.
But that is my guess- either a halfmoon or a delta unless you can get one of him from the side and him flaring at a mirror to make a positive identification.