A geometry problem by Nick Okita

A straight cylinder of height h=1 cm has its basis on the xy plane defined by: $x^2 + y^2 - 2x - 4y + 4 \leq 0$

Another plane containing the line $y - x = 0$ and parallel to the cylinder axis, cuts it in two solids. Calculate the surface area of the smaller solid.

Use, if necessary: $π=3, \sqrt{2}=1.4, \sqrt{3}=1.7, \sqrt{5}=2.2$

This was slightly modified from a question of ITA-Brazil 2013-2014 Entrance Exam