Area formula for $n$-gon Is there a formula for the area of a general polytope with $n$ vertices which just uses the distances between vertices, like Herons formel for the area of a triangle?

In general, the area of an $n$-gon cannot be deduced from the distances between vertices alone. For example, the two $8$-gons

!n-gons with different areas

have the vertices in the same places (and thus the distances between vertices will be the same), but will have different areas.