Consider the following formula for finding the area of an arbitrary planar polygon: $$ A=N\odot\sum_{i=0}^{n-1}\left(\frac{P_i\times P_{i-1}}{2}\right)$$
Where N = the plane's normal, and Pi represents each point of the polygon.
What does the little circle with the dot mean? I'm a bit confused by this formula because I expect the answer to be a number, but how would I multiply two vectors? I am assuming the circle with a dot is multiplication, but I really have no idea.
This equation comes from this site:
http://paulbourke.net/geometry/polygonmesh/
about 2/3rds down the page for calculating the area of a 3d polygon.
It almost certainly represents the "dot product", and this is merely an unconventional notation for that.
(I say "almost certainly" because when it's interpreted as a dot-prod, the formula correctly computes the area, and I cannot think of any other interpretation that yields the same result. Just to be clear: the computation generates the signed area of the polygon, i.e., it may be positive or negative depending on whether the vertices, viewed in order looking in direction $N$, form a clockwise or counterclockwise sequence.)