What is the area of the marked region?



The marked region is a right triangle ,see with height \(\dfrac{\sqrt{3}}{2}\), see and base \(\dfrac{1}{2}\).
Hence its area equals \[\dfrac{\sqrt{3}}{2}\cdot\dfrac{1}{2}\cdot\dfrac{1}{2}=\dfrac{\sqrt{3}}{8}\,.\]