What is the area of the marked triangle?



The marked triangle has one side in common with the small equilateral triangle.
The length of this side is \(\dfrac{1}{2}\).
The height of the marked triangle is half of the height of the big equilateral triangle, namely \[\dfrac{1}{2}\cdot \dfrac{\sqrt{3}}{2}=\dfrac{\sqrt{3}}{4}\,.\] So the area of the marked triangle is \[\dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{\sqrt{3}}{4}=\dfrac{\sqrt{3}}{16}\,.\]