What is the area of the marked triangle?



The big equilateral triangle has side length \(1\).
The marked triangle is a rescaling of it by the factor \(\dfrac{2}{3}\).
So the marked triangle has side length \(\dfrac{2}{3}\).
The area of the marked triangle is then \[ \dfrac{\sqrt{3}}{4} \cdot \dfrac{4}{9} = \dfrac{\sqrt{3}}{9}\,.\]