Kite in a Square

Can you make sense of the three methods to work out what fraction of the total area is shaded?
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Problem

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:

Image
Kite in a Square


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?

 

Image
Kite in a Square

 

Coordinates approach

 

 

Image
Kite in a Square

 

Similar Figures approach

 

 

Image
Kite in a Square

 

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.