$h=\sqrt{2^2-1^2}=\sqrt{3}\left[cm\right]$

$P_p=6\cdot \frac{1}{2}\cdot 2\cdot \sqrt{3}=6\sqrt{3}\left[c{m}^2\right]$

$P_b=6\cdot 2\cdot b=12b\left[c{m}^2\right]$

$12b=6\sqrt{3}\mid :12$

$b=\frac{1}{2}\sqrt{3}\left[cm\right]$