, 2015

A square ink pad has sides of length 1 cm. It is covered in black ink and carefully placed in the middle of a piece of white paper. The square pad is then rotated $180°$ about one of its corners so that all of the pad remains in contact with the paper throughout the turn. The pad is then removed from the paper. What area of paper, in $cm^2$, is coloured black?

(A) $\pi+2$ (B) $2\pi-1$ (C) $4$ (D) $2\pi-2$ (E) $\pi+1$