MathNet 2021 — Part 08 Question 46

Question 46

A square of side length $2$ is divided into four triangles, two of which are isosceles, as shown. The area of one of the isosceles triangles is twice the area of the other. What is the area of the shaded triangle?

Question illustration

$\frac23$
$\frac{\sqrt2}{2}$
$\frac8{13}$
$2-\sqrt2$
$\frac{3-\sqrt2}{2}$