What is the length of the marked segment?



The marked segment is the hypotenuse of a right triangle whose legs have length \(\dfrac{1}{2}\).
By Pythagoras's theorem, the hypotenuse has length \[\sqrt{\Big(\dfrac{1}{2}\Big)^2+\Big(\dfrac{1}{2}\Big)^2}=\dfrac{\sqrt{2}}{2}\,.\]