Shaded square

Weekly Problem 41 - 2016
The diagram shows a square, with lines drawn from its centre. What is the shaded area?

Problem

Image
Shaded Square


The diagram on the right shows a square with side length $2\text{m}$ and lines drawn to its sides from its centre $O$. The points $A$, $B$, $C$ and $D$ are all on different sides of the square.

The lines $OA$ and $OB$ are perpendicular, as are $OC$ and $OD$.

What is the shaded area?

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