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10 votes
Accepted

Professor Rackbrane: Count the triangles

We distinguish the triangles by how many of the short sides (ABCDEA) they use:
Parcly Taxel's user avatar
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6 votes

Professor Rackbrane: Count the triangles

I have a general method for counting triangles in an given figure.
Florian F's user avatar
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3 votes

Professor Rackbrane: Count the triangles

At OP's request, here's another way of organizing the calculation. I don't claim that it's any better than the others already presented in other answers.
Gareth McCaughan's user avatar
3 votes

Professor Rackbrane: Count the triangles

There are: note giving meaning same reasoning might also help for other, similar, figures, and, perhaps, not only for counting triangles. note about counting triangles
FirstName LastName's user avatar
3 votes

Professor Rackbrane: Count the triangles

Here is a slightly different solution which focuses on vertices:
Will.Octagon.Gibson's user avatar

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