Polygon area

Euclid’s equal areas, Heron’s formula, and Pick’s theorem, all checked against the shoelace formula.

Euclid’s Elements, Book I: equal areas between parallels

Euclid's Elements, Book I: equal areas between parallels

Heron’s formula and needle-like triangles

Heron's formula and needle-like triangles

Pick’s theorem: area from lattice points

Pick's theorem: area from lattice points