I have my eye on a 40" 12hp Murray riding mower, it's maybe 10 years
old or so, regular front-engine standard tractor mower. My house is
built on a hill, and I'm wondering if the slope is too great. Due to
the shape of my yard, I can't really go up and down the hill, I have
to go across the hill. I'd guess the hill is a bout 20 degrees, and
I'm nervous that the mower with me sitting on it will be too top-heavy
and flip. Or is the center of gravity pretty low in these things?

Thanks,
BTW how big an area is to be mowed? Anything up to say half an acre,
depending on on obstructions/trees etc. etc. should be pretty easy to
do with a 'walk behind' gas mower?
We use a plain old 3.5 HP gas one for about quarter acre. I'm in mid
70s.
Now typically about $150 new? Sharpening the blade yesterday looked
like the shaft might be slightly bent? Or maybe the hub is crooked?
Son in law, mid 40s, has bought one with about one more HP than mine
which has that drive mechanism to its front wheels. Not that keen on
it although it happens to be a model that cuts closer to fence edges
etc. cos it sometimes seems to be running away from you! It's also a
little heavier than the 'plain old' and with the drive engaged harder
to manoeuvre on slight slopes etc.
A ride-on must be much heavier and be harder and larger to store
during the winter?