(48) Shoelace Method For Determining A Polygon's Area

[gerry_in_polo]

Shoelace Method for determining the area enclosed by any polygon. Enter the (X,Y) coordinates of the N polygon corners in a 2xN matrix and run the program. Example enter the following matrix of (X,Y) coordinates:

[[2 5]
[7 10]
[12 20]
[8 12]
[4 3]]

The polygon area calculated by the program is 10.5

[Thomas Klemm]

This program works as well for the HP-48:

Code:

\<<
  DUP HEAD +
  2 \<< CROSS \>> DOSUBS
  \GSLIST ABS 2 /
\>>

However the pair of coordinates are expected in a list.

Example:
{
[ 2 5 ]
[ 7 10 ]
[ 12 20 ]
[ 8 12 ]
[ 4 3 ]
}

Area = 10.5