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keisanHigh-precision calculations for everyday life and work

Area of a polygon bounded by coordinate points

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Calculates the area and perimeter of a polygon bounded by arbitrary coordinate points.
The number of coordinate points can be changed.
Coordinate point
j
1
2
3
4
5
Area S9
Perimeter L15.546774330981
\(\normalsize Polygon\ surrounded\ with\ any\ points\\ (1)\ area:\\ \hspace{20px}S=\frac{1}{2}\left|{\large\displaystyle \sum_{\small j=1}^{n}}(x_j-x_{j+1})*(y_j+y_{j+1})\right|\\ (2)\ perimeter:\\ \hspace{20px}L={\large\displaystyle \sum_{\small j=1}^{n}}\sqrt{(x_j-x_{j+1})^2+(y_j-y_{j+1})^2}\\ \hspace{80px}x_{n+1}=x_1,\ y_{n+1}=y_1\\\)

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