What is the length of the marked segment?



The marked segment is the hypotenuse of a right triangle whose legs have lengths \(1\) and \(\dfrac{1}{2}\) respectively.
By Pythagoras's theorem the hypotenuse has length \[\sqrt{1^2 + \Big(\dfrac{1}{2}\Big)^2}=\dfrac{\sqrt{5}}{2}\,.\]