Heron’s Formula
Triangle area from three sides.
Key idea
Triangle area from three sides.
In depth
When you know all three sides a, b, c, compute s = (a + b + c)/2 and then A = √(s(s − a)(s − b)(s − c)). It saves finding a height.
Worked example
Sides 13, 14, 15: s = 21, A = √(21 × 8 × 7 × 6) = √7056 = 84.
Formula
Real-world uses
- Finding the area of a triangular plot when only the three side lengths are measured
Common mistake
Using the perimeter instead of the semi-perimeter s.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Heron’s Formula?
Triangle area from three sides. It is a topic at the advanced level in Geometry.
What is the formula for Heron’s Formula?
The key formula is A = √(s(s−a)(s−b)(s−c)).
Where is Heron’s Formula used in real life?
Real-world examples: Finding the area of a triangular plot when only the three side lengths are measured.
What should I learn before Heron’s Formula?
Make sure you are comfortable with Area of Triangle, the previous topic in Geometry.
What is a common mistake with Heron’s Formula?
Using the perimeter instead of the semi-perimeter s.
How can I practise Heron’s Formula?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Heron’s Formula?
Move on to Area of Trapezoid next.
Related advanced topics in Geometry
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.
- Cones – Volume and surface area of a cone.