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Kite in a Square

Age 14 to 18
Challenge Level

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?

This printable worksheet may be useful: Kite in a Square

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.