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Tilted Squares

Age 11 to 14
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
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Tilted Squares printable sheet


It's easy to work out the areas of squares drawn on a grid if they are oriented in the usual way:

 squares with area 1,2,3 and 4


 
Can you find a quick and easy method to work out the areas of tilted squares?
 
Here are some squares with a tilt of 1:

squares with tilt 1
See the hint for suggested ways to calculate their areas.


Notice anything special about their areas?
Can you predict the areas of other squares with a tilt of 1?
 
What about squares with a tilt of 2? Or 3? Or 4? Or...?
Notice anything interesting?

Can you make any conjectures about the areas of tilted squares?
Can you prove your conjectures?

You might like to use the interactivity below to help you to draw tilted squares.

Full Screen tablet/mobile friendly version

 

 

 

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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