Four Square

Weekly Problem 17 - 2015
A square contains two overlapping squares. What is the total of the shaded regions?
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Problem

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Four Square
 

The square ABCD has an area of 196. It contains two overlapping squares; the larger of these squares has an area 4 times that of the smaller and the area of their overlap is 1.

What is the total area of the shaded regions?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.