Triangles' triangle

Image

The perimeter of the large triangle is $24 \; \text{cm}$, so it has side of length $8 \; \text{cm}$, so each small triangle has side of length $1 \; \text{cm}$. So each small triangle has perimeter $3 \; \text{cm}$

$$\begin{array}{rcl}\text{Total length of black lines}& =& \text{Total perimeter of shaded triangles}\\ & =& \text{Number of shaded triangles}\times 3\text{cm}\\ & =& 27\times 3\text{cm}\\ & =& 81\text{cm}\end{array}$$