In the figure you provided, we can identify several right-angled triangles that involve the point $H$, particularly the line segment $HD$. The problem describes a triangular prism and the specific points and distances provided allow us to consider certain triangles. Let's analyze possible right-angled triangles that could involve $HD$.

Relevant information:

• $\triangle ABC$ is right-angled at $B$.
• $AB = BC = 100 \, \text{cm}$, $CF = DE = 40 \, \text{cm}$, and $BH = 57.5 \, \text{cm}$.