A method for calculating the area of a triangle when you know the lengths of all three sides. Let a,b,c be the lengths of the sides of a triangle. The area is given by:

where p is half the perimeter, or

Heron was one of the great mathematicians of antiquity and came up with this formula sometime in the first century BC, although it may have been known earlier. He also extended it to the area of quadrilaterals and higher-order polygons.

Related triangle topics

General

• Triangle definition
• Hypotenuse
• Triangle interior angles
• Triangle exterior angles
• Pythagoras' Theorem
• A graphical proof of Pythagoras' Theorem
• Pythagorean triples
• Area of a triangle
• Triangle circumcircle
• Triangle incircle
• Triangle inequality
• Triangle medians
• Midsegment of a triangle
• Heron's formula

Triangle types

• Right triangle
• Isosceles triangle
• Scalene triangle
• Equilateral triangle
• Obtuse triangle
• Acute triangle
• 3-4-5 triangle
• 30-60-90 triangle
• 45-45-90 triangle

Triangle centers

• Incenter of a triangle
• Circumcenter of a triangle
• Centroid of a triangle
• Orthocenter of a triangle

Congruence and Similarity

• Congruent triangles

Triangle quizzes and exercises

• Triangle type quiz
• Ball Box problem
• How Many Triangles?
• Satellite Orbits