KöMaL 2019 C1563

Let us consider one half of an equilateral triangle (that is, the triangle having angles $30^\circ$, $60^\circ$ and $90^\circ$). We create two more triangles by rotating the original one by $30^\circ$, and the original one by $60^\circ$ about its right angle in both cases. Determine the area of the intersection of these 3 triangles.