Prospettiva:
Area sottesa divisa in trapezi, cioe' vederci un "politrapezio".
"Politrapezio" e' un mio neologismo.
Area del trapezio e del politrapezio.
l'area del politrapezio e' data dalla formula
| A= | 1 2 |
| | x1 | x2 | ... | xn | | | +xnyn -x1y1 |
| y1 | y2 | ... | yn |
But what does that mean? The notation is meant to be suggestive of a determinant. It’s not literally a determinant because the matrix isn’t square. But you evaluate it in a way analogous to 2 by 2 determinants: add the terms going down and to the right, and subtract the terms going up and to the right
(x2-x1)(y1+y2) +x2y1 +x2y2 -x1y1 -x1y2
(x3-x2)(y2+y3) +x3y2 +x3y3 -x2y2 -x2y3
(x4-x3)(y3+y4) +x4y3 +x4y4 -x3y3 -x3y4
(x5-x4)(y4+y5) +x5y4 +x5y5 -x4y4 -x4y5
(x6-x5)(y5+y6) +x6y5 +x6y6 -x5y5 -x5y6
(x1-x6)(y6+y1) +x1y6 +x1y1 -x6y6 -x6y1 caso poligonale chiusa
Surveyors formula for area of a polygon https://www.johndcook.com/blog/2018/09/26/polygon-area/