This rectangular prism is intersected by a plane that contains points B, D, H, and F.

perimeter = BD + DH + HF + FB

 

BD = HF      and     DH = FB

so...

perimeter = HF + FB  + HF + FB

perimeter = 2HF + 2FB

 

7² + 8² = HF²   →   HF = \(\sqrt{113}\)     cm

FB = 6     cm

 

perimeter = 2\(\sqrt{113}\) + 2(6)

perimeter = 2\(\sqrt{113}\) + 12

perimeter ≈ 33.3     cm