Innocent Bystander posted:
It suggested to me that the four triangles in this basic shape will always be equal regardlee of the sizes of the squares - so as on this occasion I’d used a spreadsheet to do the calcs, before closing I substituted three random numbers for the areas of the squares - and yes, indeed, the four triangles come out with the same areas.
It's true that all 4 triangle will have the same area. In the case of Farmer Watts, this was 9 acres. This provides a very satisfying solution to the overall acreage of 100.
But putting any three square fields together in the form of the initial triangle, then adding the three external triangles leads to four new fields, each with the same area.
I haven't been able to find a neat set of initial fields, other than the 26, 20 and 18 that gives such a satisfyingly precise overall acreage as 100. One or two close ones, but not 100.