Given a triangular prism with side lengths of the base as a, b, and c, and height h, then the lateral surface area, A is given by
[tex]A=(a+b+c)h[/tex]
In our case,
[tex]a=5m,b=6m,c=7m,\text{ and }h=12.5m[/tex]
Hence,
[tex]A=(5+6+7)12.5=18\times12.5=225m^2[/tex]
Therefore, the lateral surface area in square meters is 225
