Dividing a square

A square is divided into three shapes which all have equal areas. Can you find the length of this side?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative
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