What is the area of the marked triangle?



The basis of the marked triangle has length \(\dfrac{1}{3}\) because it is a side of the small equilateral triangle.
The height of the marked triangle equals the height of the big equilateral triangle minus the height of the small equilateral triangle.
So it is \(\dfrac{\sqrt{3}}{3}\).
The area of the triangle is then \[\dfrac{1}{2}\cdot \dfrac{1}{3}\cdot \dfrac{\sqrt{3}}{3}=\dfrac{\sqrt{3}}{18}\,.\]