Total area: sum of all i < j, k < l, with (x(j) - x(i)) * (y(l) - y(k))

Note that because (i,j) pair is independent of (k, l) pair, we can break up the sum and associate each of them with each dimentions!!! i.e., the final answer becomes

sum of all i < j x(j) - x(i)

times

sum of all k < l y(l) - y(k)

To calculate each sum term, we notice that for each item i, it appears (i - 1) times as the LHS of the delta, and n - i times as the RHS of the delta, i.e.,

sum over all i, (i - 1) x(i) - (n - i) x(i) = (2 * i - n - 1) * x(i) !