Paper puzzle

Here's an easy puzzle, if you have all the facts to hand.

If you cut two A4 sheets of paper along the diagonal, you can arrange the
four triangular pieces into a square, with the pieces touching, but not
overlapping and the diagonals forming the outer edge of the square. There
will be a small uncovered area in the centre of this arrangement.

What proportion of the area of the larger square does the central
uncovered square area form?

--
David Entwistle