Variance of the longer piece of a cut rope

A rope one metre long is cut at a single point chosen uniformly along its length. What is the variance, in square metres, of the length of the longer of the two pieces?

$\tfrac{1}{48}$. If the cut is at $U\sim\text{Unif}(0,1)$, the longer piece is $\max(U,1-U)$, which is uniform on $[\tfrac12,1]$ because each value $c$ there arises from exactly two equally likely cut points. A uniform on an interval of length $\tfrac12$ has variance $\tfrac{(1/2)^2}{12}$.