Heron's Formula

triangle sss

Area of a Triangle from Sides

You can calculate the area of a triangle if you know the lengths of all three sides, using a formula that has been known for nearly 2000 years.

It is called "Heron's Formula" after Hero of Alexandria (see below)


Just use this two step process:

Step 1: Calculate "s" (half of the triangles perimeter):   s = (a+b+c)/2
Step 2: Then calculate the Area:   herons formula A = sqrt( s(s-a)(s-b)(s-c) )

Example: What is the area of a triangle where every side is 5 long?

Step 1: s = (5+5+5)/2 = 7.5
Step 2: A = √(7.5 × 2.5 × 2.5 × 2.5) = √(117.1875) = 10.825...

Try it yourself:



In the calculator above I also used the Law of Cosines to calculate the angles (for a complete solution). The formula is:

triangle angle from sides C = cos^-1( (a^2+b^2-c^2)/2ab )

Where "C" is the angle opposite side "c".