Volume of the pyramid...

Question

I have such a problem from geometry:

Five edges of a regular triangular pyramid have the length of $6$ $dm$, but the sixth- $4$ $dm$. Determine the volume of the pyramid.

For me the problem is quiet confusing, because I do not know where falls the projection of the top of the pyramid on it's base. If it were on inscribed circle , than the things are obvious, but as I observe it's not so. Can you please give me an advise?

Thank you!!!

Answer 1

See the figure below:

1. Find out $DE$ and $BE$.
2. Find out $DF$.
3. Find out the volume of the pyramid.