In the picture, there is a triangular grid, and within it, there are four polygons. The perimeters of polygons $A, B$, and $D$ are $56 \mathrm{~cm}, 34 \mathrm{~cm}$, and $42 \mathrm{~cm}$, respectively.

Determine the perimeter of triangle $C$.

(K. Pazourek)

![](https://cdn.mathpix.com/cropped/2024_04_17_ebb0cc8ff65c04bed773g-1.jpg?height=225&width=1128&top_left_y=1435&top_left_x=470)

Hint. What is the length of one horizontal segment of the triangular grid?
The perimeters of polygons $A$ and $B$ differ by two horizontal segments, which corresponds to $56-34=22(\mathrm{~cm})$. One horizontal segment is therefore $11 \mathrm{~cm}$ long.

The perimeter of polygon $D$ consists of two horizontal segments (-) and four backward-sloping segments $(\backslash)$, which together amount to $42 \mathrm{~cm}$. These four backward-sloping segments have a total length of $42-22=20(\mathrm{~cm})$, so one is $5 \mathrm{~cm}$ long.

The perimeter of polygon $B$ consists of one horizontal (-), three backward-sloping $(\backslash)$, and one forward-sloping (/) segment, which is $34 \mathrm{~cm}$. One forward-sloping segment is therefore $34-11-3 \cdot 5=8(\mathrm{~cm})$ long.

The perimeter of triangle $C$ is equal to $11+5+8=24(\mathrm{~cm})$.