PostGIS

To work with PostGIS data types such as geometry or geography, you’ll need to install PostGIS first.

-- Activate the postgis module in the current database
create extension if not exists postgis;

create table coverage (
  id int primary key,
  name text unique,
  area geometry
);

insert into coverage (id, name, area) values
  (1, 'small', ST_GeomFromText('POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))',4326)),
  (2, 'big', ST_GeomFromText('POLYGON((0 0, 10 0, 10 10, 0 10, 0 0))', 4326);

application/geo+json

PostgREST supports the standard application/geo+json media type which can be used to get the output in GeoJSON format. This will work for PostGIS versions 3.0.0 and up and will return the output as a FeatureCollection Object:

curl "http://localhost:3000/coverage" \
  -H "Accept: application/geo+json"

{
  "type": "FeatureCollection",
  "features": [
    {
      "type": "Feature",
      "geometry": {
        "type": "Polygon",
        "coordinates": [
          [[0,0],[1,0],[1,1],[0,1],[0,0]]
        ]
      },
      "properties": {
        "id": 1,
        "name": "small"
      }
    },
    {
      "type": "Feature",
      "geometry": {
        "type": "Polygon",
        "coordinates": [
          [[0,0],[10,0],[10,10],[0,10],[0,0]]
        ]
      },
      "properties": {
        "id": 2,
        "name": "big"
      }
    }
  ]
}

Using generated columns

If you need to add an extra property, like the area in square units by using st_area(area), you could add a generated column to the table and it will appear in the properties key of each Feature.

alter table coverage
  add square_units double precision generated always as ( st_area(area) ) stored;

In the case that you are using older PostGIS versions, then creating a function is your best option:

create or replace function coverage_geo_collection() returns json as $$
  select
    json_build_object(
      'type', 'FeatureCollection',
      'features', json_agg(
        json_build_object(
          'type', 'Feature',
          'geometry', st_AsGeoJSON(c.area)::json,
          'properties', json_build_object('id', c.id, 'name', c.name)
        )
      )
    )
  from coverage c;
$$ language sql;

Now this query will return the same results:

curl "http://localhost:3000/rpc/coverage_geo_collection"

{
  "type": "FeatureCollection",
  "features": [
    {
      "type": "Feature",
      "geometry": {
        "type": "Polygon",
        "coordinates": [
          [[0,0],[1,0],[1,1],[0,1],[0,0]]
        ]
      },
      "properties": {
        "id": 1,
        "name": "small"
      }
    },
    {
      "type": "Feature",
      "geometry": {
        "type": "Polygon",
        "coordinates": [
          [[0,0],[10,0],[10,10],[0,10],[0,0]]
        ]
      },
      "properties": {
        "id": 2,
        "name": "big"
      }
    }
  ]
}

Using string representation

To insert areas in polygon format, you can use string representation:

curl "http://localhost:3000/coverage" \
  -X POST -H "Content-Type: application/json" \
  -d @- << EOF
  [
    { "id": 3, "name": "strip", "area": "SRID=4326;POLYGON((0 0, 50 0, 50 2, 0 2, 0 0))" },
    { "id": 4, "name": "diamond", "area": "SRID=4326;POLYGON((5 0, 10 5, 5 10, 0 5, 5 0))" }
  ]
EOF

PostgREST will automatically cast the area column into a Polygon geometry type.