A formula for the area of a triangle: Useless, but explicitly in Deep Sets form

Any permutation-invariant function of data points vecri can be written in the form ρ(sumiφ(vecri)) for suitable functions ρ and φ. This form - known in the machine-learning literature as Deep Sets - also generates a map-reduce algorithm. The area of a triangle is a permutation-invariant function of the locations vecri of the three corners 1≤ i≤ 3. We find the polynomial formula for the area of a triangle that is explicitly in Deep Sets form. This project was motivated by questions about the fundamental computational complexity of n-point statistics in cosmology; that said, no insights of any kind were gained from these results.