For a few extra dollars you can have Home Depot do all your cuts for you, or use their equipment to cut the sheets yourself. It is best to draw up a diagram of the cage you want to build so you can take in account the width of the wood itself. Also the saw does 'eat' about a 16th of an inch per cut.
Typical thickness of a melamine sheet is 5/8ths of an inch. Thus the top and bottom piece needs to be the full length of the cage, plus 5/8ths x 2 (to ensure the top and bottom piece fit snug with the top of the end pieces (and bottom).
Melamine needs to be pre-drilled to prevent splintering and 'popping' of the screw or nail as it comes out. Ends may need to be covered with 'stripping' which you can buy at the same place you buy the wood. This stripping is basically plastic sticky stuff to coat the 'naked' ends of the board when cut. You don't need to use it but it gives a nicer finish. It also protects from humidity getting into the wood and causing it to swell.
Excess dampness is melamine's enemy. Good to seal the insides with an aquarium safe caulking too.
Malamine is basically particle board coated with a vinyl 'finish'. Particle is what my dad calls, sawdust and glue. Get it wet and it swells like a sponge and the glue breaks down..so even if completely dry, it still messed up.
That said, it is one of the most common building materials used for cages and works very well. It is also what most shelving units you buy assembled or not, (including desks, computer desks, and other similar furniture), so definitely a very effective building material that has little finishing work to do. Basically cut, screw together, touch up edges, done.
Plywood would require sanding, varnish or paint, sealed with something to keep water out (several coats of clear varnish, or sealer ontop of stain or paint)
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PHLdyPayne