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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

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2


If you take the side length of the 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. 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.