Your question is very broad and the answer depends on the room, the carpet style and material, and your budget. A custom made carpet will cost more since even if it's made from lower cost material it will need to be professionally installed as opposed to a ready-made standard area rug. A 100% wool rug will be more expensive than a synthetic one. A smaller room may look and feel larger with wall-to-wall carpet since you're not chopping up the floor. What flooring is in the room now, hardwood, tile, vinyl, a plywood subfloor only? Are you considering a pattern or a plain carpet?

Perhaps show a photo of the room and a scaled floor plan to get better advice.

Any carpet shop will cut to size and can have any carpet bound on four sides and can be used as an area rug. Quality then becomes what you choose. We had this done for a family room. It was 30+ years ago.

Is this a wall to wall rug or just area rugs? I often ignore the idea that the feet of furniture needs to sit on a rug at all so post pics of the spaces and a bit more info. Add the pics and info to a comment here.

I do this all the time, as rarely is a "standard" perfect in very large or oddly proportioned rooms.

You don't have enough context to answer your question. What is the room, Or the multiple of those, the dimensions,?

What sort of budget?

A custom size, right down to the inch, can be done in nylon broadloom, can be done in wool, can be done in sisal.....can be literally anything you would install edge to edge in a space. Truth is man, many new broadloom, patterned, thicker, more textured, more luxurious ? Are meant for exactly this purpose and is by design, courtesy of the broadloom industry who long ago recognized a trend to more hardwood flooring in homes.

What sort of finished edge? It can be hand bound, where you have to squint to see the finish, it can be inexpensively machine bound ( not recommended ) as you see carpet samples in a flooring store. It can be ordered from the mill, and serged as many broadloom offer that option.

Add a lot more context to your question for better answers. Add pictures, and best is a drawing of the actual spaces with dimensions for all walls, and openings,

Every rug here? Custom to the inch...all from broadloom and most from those with a 15' width... not 12, nor even 13'6"

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for me, off the rack area rugs suit my style, I prefer options and when I want to change things up, the rug is generally the first thing I change. I never want to feel like I need to hold on to something I spent too much money on. It's a personal choice.

Buy a rug to mark the seating area, not the shape of the room.

https://www.jaipurrugs.com/blog/rugs-for-odd-shaped-rooms-designers-guide

I've had carpet remnants bound to fit our family room. In that case I had it cut to fit within an inch of each wall because this was on a floor that is below ground level with the result that it gets very cold in winter even when using a carpet pad. Using a remnant made this a very economical purchase. These rugs held up as well as any carpet, but actually were less hassle to replace. The downside was that I used remnants, but even for a small local store I had plenty of choice.

^ agreed I’ve used remnants in my sons’ rooms to save money and they wore like iron - still look great all these years later

I need pictures and the OP needs to come back with them. No real info at all

Sometimes the cut to shape broadloom carpets make sense in a room with an angled fireplace wall.