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):|
|Step 2: Then calculate the Area:|
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:
Where "C" is the angle opposite side "c".