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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

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Kissing Triangles

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

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Hallway Borders

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

Cuboid Faces

Age 11 to 14 Short Challenge Level:

The faces of a cuboid have areas of 12, 18 and 24 square centimetres.

What is the volume of the cuboid?


This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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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