What is the area of the marked triangle?



The marked triangle is an equilateral triangle.
Indeed, it has one angle in common with the big equilateral triangle.
Moreover, it is isosceles because two of its sides are half of the sides of the big equilateral triangle.
The marked triangle is equilateral and it has side length \(\dfrac{1}{2}\).
So its area is \[\dfrac{\sqrt{3}}{4} \cdot \dfrac{1}{4} = \dfrac{\sqrt{3}}{16}\,.\]