Heron's formula

Heron's formula gives a triangle's area from its three side lengths: the square root of s(s−a)(s−b)(s−c), where s is the semiperimeter.

Triangle area: The measure of the two-dimensional region enclosed by a triangle. Heron's formula is a way to calculate this area without knowing a height.
Triangle: A polygon with three sides and three interior angles. Heron's formula applies to this shape and no other polygon directly.
Heron of Alexandria: A Greek mathematician and engineer who lived in Roman-era Alexandria. His work gives the formula its conventional name.
Surveying: The measurement and mapping of land, boundaries, and positions. Surveyors can calculate triangular areas from measured side lengths.
Semiperimeter: Half the perimeter of a polygon. It supplies the central quantity s in Heron's formula.
Side (geometry): A line segment forming part of the boundary of a polygon. The formula takes the lengths of all three triangle sides as its inputs.
Metrica: A mathematical work by Heron of Alexandria on measurements of geometric figures. It contains the surviving ancient account associated with the area formula.
Triangulation: A method of locating positions or measuring distances using networks of triangles. Measured triangle sides can yield enclosed areas through Heron's formula.
Law of cosines: A relation connecting a triangle's side lengths to the cosine of one of its angles. It links the three given sides to the angle used in a geometric derivation.
Perimeter: The total length of the boundary of a two-dimensional shape. The semiperimeter in Heron's formula is half the triangle's perimeter.

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