12. The pattern shown in the diagram is constructed using semicircles. Each semicircle has a diameter that lies on the horizontal axis shown and has one of the black dots at either end. The distance between each pair of adjacent black dots is $1 \mathrm{~cm}$. The area, in $\mathrm{cm}^{2}$, of the pattern that is shaded in grey is $\frac{1}{8} k \pi$. What is the value of $k$ ?
12. 121 Take each shaded semi-annulus that is below the line and reflect it in the line then move it one centimetre to the left. A shaded semicircle of diameter $11 \mathrm{~cm}$ is obtained. Therefore the whole shaded area is $\frac{121}{8} \pi$. Hence the value of $k$ is 121 .