The area needed is arbitrary because it depends very much on how well you manage your Aquaponics garden, the types of crop grown and so on. Also, efficiency improves as the garden gets bigger. What crop to grow, how many to plant, when, how often? Your local climatic conditions play a major part in the equation. Serious planning and attention is required to make it happen.
It is generally accepted, by working a regular soil garden you will need 30 sqm (320 sqf) to feed a typical family of 4. That will then be 7.5 sqm (80 sqf) per person. I believe that an Aquaponic garden is much more efficient than a regular garden so the growing area required will be less.
We have spent a long time thinking about this question and observing what we can and have achieved over the last 8 years and we believe 23 sqm (250 sqft) of AP gardening space is needed to feed a family of 4.....with all the skill and attention needed to make the garden sing. So, that is approx 6 sqm (62 sqft) per person.
Aquaponics is still a garden, and successful gardening requires time and dedication.
This INDY 23 plan set is the result of 8 years of practical AP, full time 7 days a week. 23 sqm (250 sqf) of growing area spread over three different growing methodologies to produce a wide variety of produce and a realistic number of fish dinners.
If you want to be serious about food production for your family this is the minimum required.....sorry. And if you seriously do want to produce a really big chunk of your family food needs, a few other things like a half dozen egg laying chickens, some space for fruit trees and so on will need to be added to the project. Let's take a realistic approach to home grown, chemical free, nutrient dense food.
But, to move toward this goal step by step, and to produce what you can, to acquire the skills needed takes time and effort. Start to produce what you can in the time and space you have available to you.
Take the time to acquire good sound knowledge. Frankly, watching a dozen or so You Tube clips made by people who started Aquaponics a few weeks before probably won't cut it...sorry. Buy a book or a DVD from a good reliable experienced source. Trouble is we see on the internet people making crazy claims, no doubt we have all seen them, "10 times the vegetables, in half the time, twice as big." 2000 lbs of vegetables from a kit made out of a couple of old IBC's, a few bits of pipe all held together with string.....
The "armchair generals"....
The magic about Aquaponics is,
#1 Aquaponics is an ECO system and the veggies and fish produced are clean nutritionally rich family food. Much, much better than "Organic".
#2 It is more efficient than a regular garden because the plants have delivered to them water and nutrients continuously 24/7. The fish grow up in a healthy protected environment.