As I said, in times of peace, it is not very big at all. Do not misunderstand me I used to live in an area of farms. I know how big 4 square miles is.
But if you have a hoards of people encroaching on your land, who are hungry, angry, determined, weaponed, etc, it’s a lot of land to try and defend. Especially if you’re by yourself, because most of your employees had to go defend their property and families from these same angry and hungry hoards. It’s a lot to defend. Don’t think that, just because you have a gun(s), that you can possibly defend a property that size effectively.
You’re not going to have employees, or many at least, to help defend you in a time of crisis, because they will busy trying to defend their own families and won’t give too much thought to you and your families.
If you had to defend anything it would be your house just like everyone else, only you would have a nice buffer zone around your house.
There are a lot of easier and better pickings than a single house out in the middle of nowhere.
A lot of isolated farms also have houses for the farm hands and their families.
Don't have to defend all of it. Mainly the house.
One thing about farms is that crops aren't ready to eat all year round. You plant a crop, look after it as it grows, harvest it, and then do something with the harvest (sell it or preserve it). After the harvest, it's either sitting in storage near the house, or it's been sold.
In the middle ages, barons didn't build a wall around their whole estates. They built a defensible castle and put the harvest and valuables inside the castle.