Area Of A Triangle Given Three Sides - Heron's Formula With Calculator
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Math Open Reference Home Contact About Subject Index Heron's Formula for the area of a triangle(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
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.
Calculator
Use the calculator on below to calculate the area of a triangle given 3 sides using Heron's formula.
Enter the three side lengths and press 'Calculate'. The area will be calculated.
| ENTER THREE SIDE LENGTHS | |
| clear | |
| clear | |
| clear | |
| Calculate Clear | |
Other triangle topics
General
- Triangle definition
- Hypotenuse
- Triangle interior angles
- Triangle exterior angles
- Triangle exterior angle theorem
- Pythagorean Theorem
- Proof of the Pythagorean Theorem
- Pythagorean triples
- Triangle circumcircle
- Triangle incircle
- Triangle medians
- Triangle altitudes
- Midsegment of a triangle
- Triangle inequality
- Side / angle relationship
Perimeter / Area
- Perimeter of a triangle
- Area of a triangle
- Heron's formula
- Area of an equilateral triangle
- Area by the "side angle side" method
- Area of a triangle with fixed perimeter
Triangle types
- Right triangle
- Isosceles triangle
- Scalene triangle
- Equilateral triangle
- Equiangular triangle
- Obtuse triangle
- Acute triangle
- 3-4-5 triangle
- 30-60-90 triangle
- 45-45-90 triangle
Triangle centers
- Incenter of a triangle
- Circumcenter of a triangle
- Centroid of a triangle
- Orthocenter of a triangle
- Euler line
Congruence and Similarity
- Congruent triangles
Solving triangles
- Solving the Triangle
- Law of sines
- Law of cosines
Triangle quizzes and exercises
- Triangle type quiz
- Ball Box problem
- How Many Triangles?
- Satellite Orbits
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