he has named these 'eutrigons' and triangles with one 120 degree angle (which he refers to as 'co-eutrigons')
he utilises unit triangles on an isometric grid
see the section on isometric areas on this blog
the relationships are straightforwardly derived from the cosine rule, substituting 60 degrees and 120 degrees but, importantly as far as appreciation is concerned, he presents justifications based on diagrams:
a 'eutrigon' is a triangle with one 60 degree angle
the eutrigon has equilateral triangles drawn on each of the sides
what is the relationship between their areas?
a dynamic version, created by Wayne Roberts:
for the co-eutrigon, this diagram is offered by Wayne Roberts:
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