What Is 3 Sides Triangle Area?
Heron's formula gives the area of a triangle when you know only the lengths of its three sides, with no need for the height or any angle. It works for every valid triangle as long as the three side lengths satisfy the triangle inequality.
The formula, credited to the Greek mathematician Heron of Alexandria, is useful whenever measuring the altitude of a triangle is difficult or impractical — such as when a side lies across a river or a steep slope.
Formula
s = (a + b + c) / 2
A = √(s(s − a)(s − b)(s − c))
Applications
- Surveying triangular plots of land where the height is hard to measure
- Computing the area of triangular trusses and roof sections in construction
- Finding material needed for triangular sails, banners, or decorative panels
- Solving geometry problems where only the three sides of a triangle are given
- Determining land parcel sizes in real estate and civil engineering
Sources
- Stewart, J. (2015). Calculus: Early Transcendentals (8th ed.). Cengage Learning.
- Coxeter, H. S. M. (1969). Introduction to Geometry (2nd ed.). Wiley.