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What fractions can you find between the square roots of 65 and 67?

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Equal Equilateral Triangles

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

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The Square Hole

Age 14 to 16 Challenge Level:


If you take the side length of the yellow equilateral triangle as the unit for length, what would be the size of the hole ?

Alternatively, if the area of the yellow equilateral triangle is taken as the unit for area, what size is the hole then ?

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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