What is the area of the marked triangle?



The big equilateral triangle has side length \(1\) hence area \(\dfrac{\sqrt{3}}{4}\).
The small equilateral triangle is a rescaling of it by a factor \(\dfrac{1}{3}\).
So its area is \[\dfrac{\sqrt{3}}{4} \cdot \dfrac{1}{9} = \dfrac{\sqrt{3}}{36}\,.\]