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Threesomes

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.

Isosceles

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

Counting Triangles

Age 11 to 14 Challenge Level:
Triangles are formed by joining the vertices of a skeletal cube.

How many different types of triangle are there?

How many triangles altogether?
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.
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