Australian AMC 2021 - Senior Question 17

Question 17

A square is divided into three congruent isosceles triangles and a shaded pentagon, as shown. What fraction of the square’s area is shaded?

Question illustration

$\frac13$
$\frac14$
$\frac{\sqrt2}{6}$
$\frac{\sqrt3}{8}$
$2-\sqrt3$