Count the valence electrons around sulfur in $SF_4$

• Sulfur has $6$ valence electrons.
• In $SF_4$, sulfur forms $4$ $S-F$ bonds.

So, around the central sulfur atom there are:

• $4$ bonding pairs
• remaining $1$ lone pair

Thus, the total number of electron pairs around sulfur is: $4 + 1 = 5$

Determine the electron-pair geometry using VSEPR theory

A central atom with $5$ electron pairs has trigonal bipyramidal electron geometry.

Since the question says including lone pair(s) of electrons, if any), we must give the geometry including the lone pair.

Therefore, the geometry of $SF_4$ including the lone pair is: $\boxed{\text{Trigonal bipyramidal}}$

Note on actual molecular shape

If the question had asked for the shape of only the atoms (excluding the lone pair), $SF_4$ would be see-saw. But that option is not given, and the question explicitly says to include lone pair(s).

Check the options

• A: Tetrahedral $\to$ incorrect
• B: Trigonal bipyramidal $\to$ correct
• C: Square planar $\to$ incorrect
• D: Pyramidal $\to$ incorrect

Final answer

$\boxed{\text{B: Trigonal bipyramidal}}$

Comparison with stored correct answer

Stored correct answer: B

My derived answer: B

They match.