Dividing a square

A square is divided into three shapes which all have equal areas. Can you find the length of this side?
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Problem

Three lines have been drawn from the centre of this square to split it into two congruent trapezia and a pentagon.

Image
Dividing a square


The side length of the square is 1, and the areas of the three shapes are all equal.

What is the length $x$?

This problem is adapted from the World Mathematics Championships