What is the area of the marked triangle?



The marked triangle is part of an equilateral triangle whose side length is \(1\).
The base is a side of the equilateral triangle, so it has length \(1\).
The triangle vertex opposite to the basis is the center of the equilateral triangle.
So the height of the triangle is \(\dfrac{1}{3}\) of the height of the equilateral triangle.
The area of the marked triangle is then \[\dfrac{1}{2} \cdot \dfrac{1}{3}\cdot \dfrac{\sqrt{3}}{2}=\dfrac{\sqrt{3}}{12}\,.\]