You may also like

Square Areas

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

Dissect

What is the minimum number of squares a 13 by 13 square can be dissected into?

2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

Square Within a Square Within...

Age 11 to 14 Short Challenge Level:
 


The diagram shows a square within a square within a square within a square. Find the fraction of the area that is shaded.







This problem is taken 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.
Copyright © 1997 - 2021. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.