Mr Red wrote: my - Grid Ref & distance & area calculator app uses the shoelace algorithm.

Does the page at that link calculate area?

I see the formula uses cartesian coordinates in a plane. Does it use OSGRs? Presumably not lat/long.

Under the old Common Agricultural Policy (CAP) landowners got payments based on field areas and crop types - or lack of crops (setaside payments). They had to fill in a form listing each field and its area. I wonder if they used this formula? Probably just knew: "the lower 5 acre meadow - that's be 2.023 hectares"

I did some surveying back in the days of theodolites and Dumpy levels. These instruments were being replaced by lasers and nowadays by DGPS. I used a tellurometer once! Never had to work out an area, though.