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Doodles

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

Russian Cubes

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

Areas and Ratios

Do you have enough information to work out the area of the shaded quadrilateral?

Kite in a Square

Age 14 to 18
Challenge Level

Kite in a Square printable sheet
 

ABCD is a square. M is the midpoint of the side AB.
By constructing the lines AC, MC, BD and MD, the blue shaded quadrilateral is formed:


What fraction of the total area is shaded?

Once you have had a think about this, you might like to take a look at these three different methods for finding the shaded area. In each case, all the statements have been muddled up. Can you rearrange them back into their original order?
 

 

Coordinates approach

 

 

 

Similar Figures approach

 

 

 

Pythagoras approach

 

 


Thanks to Jerome Foley for drawing our attention to this problem.

 

We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of this resource.

 

 

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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