OpenLayers - how do I draw a Polygon from existing lonLat points?

After a lot of experimenting, I found out how to do it:

let sitePoints = [];
let siteStyle = {
  // style_definition
};

let epsg4326 = new OpenLayers.Projection("EPSG:4326");
for (let i in coordinates) {
  let coord = coordinates[i];
  let point = new OpenLayers.Geometry.Point(coord.lng, coord.lat);
  // transform from WGS 1984 to Spherical Mercator
  point.transform(epsg4326, map.getProjectionObject());
  sitePoints.push(point);
}
sitePoints.push(sitePoints[0]);

let linearRing = new OpenLayers.Geometry.LinearRing(sitePoints);
let geometry = new OpenLayers.Geometry.Polygon([linearRing]);
let polygonFeature = new OpenLayers.Feature.Vector(geometry, null, siteStyle);
vectors.addFeatures([polygonFeature]);

OpenLayers 6

it is slightly different for OpenLayers 6, and it took ma a while to figure it out. So I paste here the relevant code for OL6.

coordinates are of type [[[number]]] (which is the GeoJson standard for polygon).

styles is out-of-scope (i can paste it here if someone is interested, but every app can define it differently).

var VectorSource = ol.source.Vector;
var {Tile, Vector} = ol.layer; //import {Tile as TileLayer, Vector as VectorLayer} from 'ol/layer.js';
var TileLayer = Tile;
var VectorLayer = Vector;

var map = new ol.Map(...);

function drawPolygonOnMap(coordinates) {
    const polygonFeature = new ol.Feature(
        new ol.geom.Polygon(coordinates).transform('EPSG:4326','EPSG:3857'));


    let source = new VectorSource({
      features: [polygonFeature]
    });

    var layer = new VectorLayer({
      source: source,
      style: styles
    });

    map.addLayer(layer);
}