Can I fit this desk in my prius prime?

It took me about a half a minute to measure mine. Measure the opening from the lowest part of the rear passenger door opening to the seat. There's your showstopper dimension before you even measure anything else. Four feet will fit either sideways on the back seat or lengthwise in the hatch area. 30 inches by 4' works, too. But not 4' X 30" X 30". The lack of vertical space is visually clear even without measuring. When you do measure it, you find that it's even less than it looks.

 

Nope. There's only about two feet between the cargo deck and the top of the back opening. I put in an eight foot long rowing machine once that was a little taller at the very front than the opening by tilting it on its side and then standing it back up after it cleared the hatch opening. I forgot how long it was but it almost touched the glove box and the hatch. It's that 30X30 that's the show stopper. 30X 24 might make it, IIRC, but just barely.

Edit to add: Can you take apart the desk?

 

If one 30" can get in the back, with the desk upside down, by tilting, would tying down the hatch be doable? Will need padding over the back 30".

Assuming this desk doesn't have a full front.