NB. compute the area of a closed polygon where
NB. the vertices are enumerated (counter-clockwise)
NB. as (x1, y1), ... (xn, yn)
NB. Method due to Goldman in "Triangles", Graphics Gems I, pp 20-23.
NB. generalized by Stone in "A Mnemonic for the Area of Polygons, American
NB. Math. Monthly 93, pp 479-480.

NB. an example polygon

[t =: 2 5$ 6 5 2 4 2 2 4 3 3 1 2

NB. the closed example polygon
[t1=: t,.{."1 t

NB. use oblique to select the major diagonal

1}. _1}. (*/"1) /. t1

area =: monad define
y. =. y. ,. {."1 y.
0.5 * (+/ 1}. _1}. (*/"1) /. |. y.)- +/ 1}. _1}. (*/"1) /. y.
)

NB. a triangle example

[t2 =: 2 3$ 0 1 0 0 0 1

NB. a rectangle example

[t3=: 2 4 $ 0 1 1 0 0 0 1 1