No, not all catamarans have trampolines. Some do and some don't. Catamarans that don't have trampolines usually have a lounge area on the bow (front) of the boat where people can sunbathe or relax. The ones that do have trampolines usually have them in the back (aft). Trampolines on catamarans serve two purposes: they provide a comfortable place to sunbathe or relax in the shade, and they act as a giant bounce pad when jumping off the boat into the water.
The size of the trampoline also varies from boat to boat. Some are large enough for several people to lie down on, while others are more like oversized mats. There are even inflatable trampolines that can be deflated and stored away when not in use.
So, if you're looking for a catamaran with a trampoline, there are plenty of options out there. Just keep in mind that not all catamarans come equipped with one – so it's always best to check before you make your purchase!