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 Skip Navigation LinksMath Help > Geometry > Polygons and Triangles > Area

Contents of the "Area" section:

Proof That Square Has Smallest Perimeter
Vector Area
Pick's Theorem
Heron's Formula
Bretschneider's Formula

Proof That Square Has Smallest Perimeter offers two different proofs that a non-square rectangle has a larger perimeter than a square with the same area.

Vector Area has several ways to find the area of a triangle and of a polygon using vectors, and a special measure similar to a determinant, but for a 2*n matrix.

Heron's Formula, Bretschneider's Formula, and Brahmagupta's Formula (part of the cyclic quadrilateral section) all give the areas of various polygons.

Related Pages in this website

Triangle Area using Determinant

Cross Product, near the bottom of the page, explains why the magnitude of the cross product of two vectors equals twice the area of the triangle formed by the vectors.

Triangle Area using Vectors Cross Products

Heron's formula for the area of a triangle, if all you know is the lengths of its sides.

Polygon Area using Determinant

 

The webmaster and author of this Math Help site is Graeme McRae.