# Heron's Formula

## 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 = \frac{a+b+c}{2}

**Step 2:** Then calculate the **Area**:

A = √s(s−a)(s−b)(s−c)

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

Step 1: s = \frac{5+5+5}{2} = 7.5

Step 2: A = √(7.5 × 2.5 × 2.5 × 2.5) = √(117.1875) = **10.825...**

Try it yourself:

images/heron.js

## Angles

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

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

2352, 2353, 2354, 2355, 3942, 3943, 3944, 3945, 3946, 2356