Farmlands and household size

[Azélor]

I was thinking doing a regional map fro my country of Guild world. I dropped the idea but would like to validate my numbers.

Initially, I planned to map the farmland on scale so I searched to find the numbers needed.
Climate is tropical borderline subtropical.
Temperatures rarely drop below 10 degrees Celsius, so food can be grown all year long (2 or 3 crops per year)
The dominant crop is rice.

The area is 31 000 sq km (water included) mostly flat. The size of Belgium.
90% of the land is used for agriculture (some areas can't be farmed) = 28 000 sq km or 2 800 000 hectare

Population is 3 000 000, a high density for medieval standard. Assuming late medieval era.
Farmers make up 80-85 % of the population = 2 400 000
Each household has 5.5 people on average (numbers taken for the Southern Song dynasty) = 436 000 households
Assuming each field is cultivated by only one family, that's 436 000 different fields and I'm definitely not going to map that. Also, each field would be 3 pixels in size at the scale I plan to use.
Each household has 2 800 000/436 000 = 6,4 hectare of land to farm.
or 64 000 m2.
There should be 15 fields per sq km.

With that land, they need to feed themselves but also produce extra food for the rest of the population.

Do these number make sense in general? I can't find any good guidelines.
Can they produce enough food?
Can they have large surpluses? so that some agricultors can use their field to grow things like tea, mulberries for silkworms, grapes for wine ...
I've read that rice fields are very labour intensive. Does it have higher yield if there are more people per field with larger fields?

[J.Edward]

One thing I have seen regarding rice fields, terraced in particular, was that some creative farmers also raised fish in the fields.
Thus they got a harvest of fish, plus the fish droppings fertilized the rice and they had higher yield from the crops planted.
And they also would eat young bamboo shoots in soup. and those were just wild, not cultivated bamboo, i think.
And then there are insects to eat. Certain grasses can be eaten as well.
An old Chinese proverb - the Chinese will eat anything on four legs except a table.
They made full use out of their environment, yet stayed mostly in harmony with it, even with huge populations.
Oh, and don't forget - rice wine.

Edit - also, the size of a meal for many people around the world is much smaller.
They may eat less times per day and less per meal, as well.
There will always be surplus, even if it must be forced, as some ruler will demand that surplus be created so they can take it.

[Azélor]

Fish in the rice fields sounds almost too good to be true.

[J.Edward]

Fish in the rice fields sounds almost too good to be true.

They do have to be careful and watchful, as that attracts birds [who will eat fish].
But that too is helpful, as the birds eat the insects that would eat the plants, as well.
There was a really good documentary on China... what was it.. from BBC.. Wild China I think.
Had loads of great info I found really helpful.