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How many triangles can you make on the 3 by 3 pegboard?

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Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

Triangles All Around

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You might like to have a look at Nine-Pin Triangles before trying this problem.

How many different triangles can you draw on a circular pegboard which has four equally spaced pegs?

What are the angles of each triangle?

If you have a six-peg circular pegboard, how many different triangles are possible now?

What are their angles?

How many different triangles could you draw on an eight-peg board?
Can you find the angles of each?

You may like to use the interactivity to try out your ideas.
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For printable sets of circle templates for use with this activity, please see Printable Resources page.

Many thanks to Geoff Faux who introduced us to the merits of the 9 pin circular geo-board.

The boards, moulded in crystal clear ABS that can be used on an OHP (185 cm in diameter), together with a teacher's guide, are available from Geoff at Education Initiatives


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.