Heron's formula for the area of a triangle

Your purchases at amazon.com support this site - Learn how

Heron's Formula for the area of a triangleAlso called Hero's Formula

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

Try this Drag the orange dots to reshape the triangle. The formula shown will re-calculate the triangle's area using Heron's Formula

(If there is no image below, see support page.)

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.

Precision

In the figure above, the area calculated is accurate. However the values shown inside the formula and on the lines in diagram are rounded off for clarity. If you use them in a calculator, you will get a slightly different answer.

Test your knowledge

What is the area of a triangle whose sides are 12, 16 and 20 meters long?	answer 96 sq meters. In the diagram above, try to create such a triangle
Challenge question: What equilateral triangle would have the same area as a triangle with sides 6, 8 and 10?	answer One where each side has a length of 7.44

Precision

Test your knowledge

Related triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Triangle quizzes and exercises